
Gass [aB i5S5 



Book ^ 



/^76 



HCovsr to Teacli. 

A 

Manual of Methods 

FOR A 

GRADED COURSE OF INSTRUCTION : 

EMBRACING THE 

SUBJECTS USUALLY PURSUED IN PRIMARY, INTERMEDIATE, GRAMMAR, 

AND HIGH SCHOOLS ; ALSO, SUGGESTIONS RELATIVE 

TO DISCIPLINE AND SCHOOL MANAGEMENT. 

FOR THE 

USE OF TEACHERS. 

BY 

HENRY KIDDLE, A.M., 

City Superintendent of Public Instruction^ New York. 

THOMAS F. HARRISON, 

I^irst Assistant Superintendent Of Grammar Schools, New York City; and Pro- 
fessor of Methods and Principles of Teaching in Saturday Normal School, 

N. A. CALKINS, 

First Assistant Superintendent of Primary Schools and Departments^ New York 

City ; and Professor of Methods and Principles of Teaching in 

Saturday Normal School, 



NEW YORK : 

J. W. Schermerhorn & Co., 

14 Bond Street. 

1875. 






Entered according to Act of Congress, in the year 1878, by 

J. W. SCIIERMERHORN & CO., 

In the Oflace of the Librarian of Congress, at Washington. 

Transfer 
Engineers school LiWi- 

June 29, 1931 



Lange, Little & Co., 

PKINTKRS, ELECTROTYPERS AND STERBOTYPEBS, 

108 TO 114 Wooster' Street, N. Y. 



PEEFAOE. 



The system of graded instruction, which has become 
so general in this country, requires for its successful 
application, the constant use, on the part of the teacher, 
of a guide, or chart, to which he may refer in order 
that his present work may harmonize with that which 
preceded, and that which is to follow it. The ground 
to be coyered in a complete course of school education, 
howeyer elementary, is quite extensiye, and hence needs 
to be diyided and subdiyided according to certain estab- 
lished principles, so that the mind of the instructor may 
not be diyerted from that which should engage his im- 
mediate attention, by the necessity of considering and 
choosing the best means of supplementing it. Such a 
graded system of teaching can best be prepared by those 
who haye had not only a long experience in the practi- 
cal business of teaching, but whose field of obseryation 
has been suflBciently comprehensiye to enable them to 
giye to the scheme an adaptability to a great yariety of 
circumstances. 

The system laid down in the work here offered to 
practical educators, whether teachers, superintendents, 
or school officers, is designed to afford such a guide as 



4 PREFACE. 

is above indicated. It is essentially the system which 
has been in use in the city of New York for some years, 
only differing from it in the number of grades into 
which the course is divided. This difference is, how- 
ever, rather nominal than real, since the number of 
grades into which a course of study is divided is en- 
tirely arbitrary, except so far as it may be dictated by 
special circumstances. Where schools are very large, 
and the attendance of pupils is fluctuating, as must be 
the case in so populous a city as New York, the neces- 
sity of constantly reorganizing classes, renders frequent 
promotions, or transfers from class to class, indispensa- 
ble, and, hence, a large number of grades becomes a 
convenience. In schools having a smaller and steadier 
attendance, the number of grades need not exceed what 
is requisite for a proper classification and division of 
subjects for simultaneous study. The order of studies 
— the main point in every course of instruction — cor- 
responds, as here arranged, precisely with the New York 
plan ; the time requisite for its completion is also about 
the same. 

This course, with its division into grades, constitutes, 
however, only the frame-work for the series of practical 
suggestions designed to assist teachers in the perform- 
ance of their professional duties — that is, in some de- 
gree, to show them what to teacTi^ as well as lioio to teach. 
All the precepts and directions here given have been 
dictated by an earnest desire to aid in the effort now 
universally put forth by the ablest and most intelligent 



PREFACE. 5 

school officers to abolish the pernicious rote method of 
teaching, by book and formula, formerly so prevalent, 
and to make universal the system which appeals, from 
first to last, to the intelligence of -the pupil, and adapts 
itself to its progressive stages of development. In the 
lower grades, the objective, or perceptive, system is, of 
course, made prominent, to be succeeded by those sub- 
jects and methods which, as they dispense to a consid- 
erable extent with the actual objects themselves, and 
appeal to the acquired ideas of the pupils, may be prop- 
erly denominated conceptive. 

The natural and physical sciences, it will be observed, 
are largely drawn upon for the materials necessary to 
accomplish this object, the sciences of observation and 
classification, such as zoology, botany, and mineralogy, 
properly taking precedence of those which require a 
more special application of the reflective and reasoning 
faculties, such as physiology, natural philosophy, and 
astronomy. By this kind of teaching, it is designed 
that the pupil shall acquire the ability to gain an ex- 
perience of his own, instead of depending exclusively 
upon that of others, and at the same time, shall acquire 
a taste for the observation and study of nature. 

Certainly such a system for the common schools of 
our country is far preferable to that which, although 
insuring proficiency in the " three Rs '^ left the pupiFs 
mind in a condition of matured stolidity, and while, 
perhaps, a most ready talking, writing, and parsing ma- 
chine, sent him forth to go through this beautiful world, 



e PREFACE. 

blind to its manifold wonders and glories/ and fit only 
to become the easy prey of the demagogue and the 
bigot. 

It is an evidence of the increasing earnestness of 
teachers, that the demand for practical suggestions 
and exact information in regard to their work is now so 
great. More especially is this so in the case of those 
engaged in primary school instruction. This depart- 
ment of teaching requires yery much special knowledge 
as well as peculiar tact to produce successful results. 
A complete exposition of the yarious methods which 
are applicable to each stage of this work would require 
a much larger space than could be devoted to it in the 
book here published. Hence, references to more full 
and complete works on the subject have been given m 
connection with several of the grades, in order to aid 
teachers in finding tlie additional information which 
they may need in this direction. 

The demand for copies of the " Manual of Instruc- 
tion and Discipline/^ recently prepared by the authors 
of this work, for the use of the primary and grammar 
schools of the city of ]^ew York, has induced them to 
endeavor to put the work into a shape in which it might 
be generally useful; and they trust that, as it is now 
presented to those engaged in practical education, it 
will prove an acceptable addition to the literature of 
American pedagogy, now so scanty and insufficient. 



COIs'TENTS. 



PAGB 

INTRODUCTION 11 



GRADED COURSE.— TENTH GRADE (Outline) 21 

How TO Teach subjects of the Tenth Geade. . . 23 
Reading (23); Phonetics (27) ; Spelling (27) ;Aritli- 
metic (29) ; Object Lessons (34) ; Drawing and 
Writing (3o) ; Management (36). 

NINTH GRADE (Outline) 37 

How TO Teach subjects of the NcsTH Geade... 39 

Reading (39) ; Phonetics (40) ; Definitions (40) ; Spell- 
ing (41); Arithmetic (41); Object Lessons (44); 
Drawing and Writing (45) ; Management (45). 

EIGHTH GRADE (Outline) 47 

How to Teach subjects of the Eighth Geade. . 49 
Reading (49) ; Punctuation (50) ; Phonetics (50) ; Def- 
initions (51) ; SpeUiQg (51) ; Arithmetic (52) ; Object 
Lessons (59) ; Drawing and Writing (61) ; Manage- 
ment (62). 



8 CONTENTS, 

PAGE 

SEVENTH GRADE (Outline) 63 

How TO Teach subjects of the Seventh Grade. 65 

Reading (65) ; Phonetics (66) ; Definitions {m) ; Aiitli- 
metic (67) ; Tables (73) ; Object- Lessons (74) ; Ge- 
ography — Preparatory Steps (80) ; Drawing and 
Writing (81). 



SIXTH GRADE (Outline) 83 

How TO Teach subjects of the Sixth Grade ... 86 
Reading (86) ; Phonetics (87) ; Definitions (87) ; Spell- 
ing (88) ; Arithmetic (88) ; Tables (92) ; Object Les- 
sons (94) ; Geography (98) ; Drawing and Writing 
(102) > General Suggestions (102). 

FIFTH GRADE (Outline) , • 105 

How to Teach subjects of the Fifth Grade . . . 107 
Reading (107) ; Spelling (110) ; Definitions (111) ; 
Arithmetic (113) ; Forms of Arithmetical Analysis 
(118) ; Tables (120) ; Geography — General Sugges- 
tions (121) ; Geography for the Fifth Grade (122) ; 
Syllabus of Topics for Geography (123) ; Correction 
of Language (125) ; Elementary Science — General 
Suggestions (126) ; Outlines of Zoology (129). 

FOURTH GRADE (Outline) 137 

How TO Teach subjects op the Fourth Grade.. 139 
Reading (139) ; Spelling (139) ; Definitions (140); Eng^ 
Irsh Grammar (140) ; Arithmetic (144) ; Syllabus 
of Topics for Common Fractions (147); Syllabus 



CONTENTS. 9 

PAGE 

for Decimal Fractions (158) ; Geography (163) ; Ele- 
mentary Science — ^Botany (164) ; Mineralogy (168) ; 
Writing (172). 

THIRD GRADE (Outline) 175 

How TO Teach subjects of the Thied Gkade... 177 
Reading (177); Spelling (178); English Grammar 
(179) ; Composifion (179) ; Arithmetic (180) ; Sylla- 
bus for Arithmetic (182) ; Geography (186) ; History 
of the United States — General Suggestions (189) ; 
Outline Sketch of the History of the United 
States (189) ; Syllabus of Topics (193) ; Physiology 
and Hygiene (194) ; Syllabus for Physiology (196). 

SECOND GRADE (Outline) 199 

How TO Teach subjects of the Second Grade.. 201 

Reading (201) ; Definitions and Word Analysis (202) ; 
English Grammar (204) ; Composition (206) ; Arith- 
metic (206) ; Syllabus for Arithmetic (209) ; Geog- 
raphy (210) ; History (211) ; Elementary Science — 
Natural Philosophy (216) ; Syllabus of Topics (220) ; 
Astronomy (221). 

FIRST GRADE (Outline) 223 

How to Teach subjects of the First Grade 225 

English Grammar (225) ; Composition (226) ; Arith- 
metic (226) ; Algebra (229) ; Geometry (232) ; Out- 
lines of Physical Geography (236) ; History, Ancient 
and Modern (238); Natural Philosophy (241); 
Astronomy (243) ; Chemistry (245) ; Book-keeping 
(250) ; Constitution of the United States (251). 



10 CONTENTS, 

PAGE 

GENERAL SUGGESTIONS RELATIVE TO CLASSI- 
FICATION AND INSTRUCTION 253 

Reviews (252) ; Progress of Classes (252) ; Progress 
of Pupils (252) ; Recitations (253) ; Lessons for 
Home Study (254); Physical Training (255) ; Man- 
ners and Morals (256). 

GOVERNMENT AND DISCIPLINE 257 

SCHOOL LIBRARY 263 



INTEODUOTIO^. 



No task can be more responsible, or require the exer- 
• else of greater care than that which has for its object 
the proper education of the young. To perform it effi- 
ciently, special preparation and study are indispen- 
sably necessary, not only in regard to the branches of 
knowledge which may have been selected as a basis for 
the instruction, but also in respect to the proper methods 
and appliances to be employed, in order to render the 
instruction truly effective. These methods niust be 
determined by a consideration of the faculties to be 
trained and educated, as well as the nature of the 
subject taught ; hence, the teacher should be familiar 
with at least the outlines of mental science, — the office 
of each of the faculties of the mind, the order in which 
they are naturally developed, and the pro;ger means of 
aiding in this development, so that the training and in- 
struction given may result in that most valuable of all 
characteristics, a well-balanced mind. It is the remark 
of Professor Hen'ry, that "the laws which govern the 
•growth and operations of the human mind are as defi- 
nite, and as general in their application, as those which 
apply to the material universe ; and it is evident that a 
true system of education must be based upon a knowl- 
edge and application of those laws/' How important 
then that the teacher should make himself familiar with 
these laws ! Certainly no true success can be obtained 



12 INTBOBTICTION, 

without this knowledge ; for destitute of it, tlie teacher 
is only an empiric, applying rules the reason of which 
he does not know, and mechanically following methods, 
the rationale of which he does not understand. 

If the teacher have suflBciently mastered these elemen- 
tary principles of his profession, it will not be difficult 
for him at all times rightly to understand his pupils^ 
mental condition and grade of advancement — a matter 
of the greatest importance, especially at the first stage 
of school instruction. Failing in this respect, many 
teachers are often found most laboriously occupied in 
the useless task of attempting to do that for the child 
which nature, without any assistance, has already ac- 
complished. They do not seem to be aware of the ex- 
tent to which the pupiFs mental faculties, more especi- 
ally these concerned in observation, have been developed 
in this way. The acquisitions made by a child of four 
or five years of age, before being placed under any regu- 
lar tuition at all, or subjected to any of the manipula- 
tions of the school teacher, are indeed wonderful. The 
senses, actively awake, have brought the young mind 
into communication with the multifarious objects of 
external nature ; the faculty of conception, peculiarly 
active in childhood, has given it a number of ideas cor- 
responding to its perceptions, and the faculty of speech 
has enabled It to connect with thousands of these ideas, 
words and combinations of words, so as to designate and 
exnress them. 

Thus is the foundation of the intellectual character 
unerringly laid by the unaided operation of nature her- 
self. Here is no senseless cramming of words, for 
words are only learned after the ideas which they repre- 
sent have been acquired. Under the guidance of a 
teacher properly conversant with the laws of the mind 



TNTRODUCTIOK 13 

and its growth, this natural process would be continued, 
and would be directed to its proper objects ; but, instead 
of this, a mental treadmill is often used, the effect of 
which is to counteract the work of nature, and check 
the mental activity of the young pupil. To learn 
A, B, C is, of course, necessary as one of the rudimen- 
tal steps of primary instruction ; but this, like every- 
thing else, should be so done, that the intelligence of 
the pupil may be fostered, not deadened, in the acquisi- 
tion. In every stage of intellectual training, let the 
teacher always remember, that his pupil's mind is not 
to be treated as a ^^ passive recipient '^ of the thoughts 
and experience of others, but as an active agent, to be 
enabled to acquire an experience of its own, and apply it 
to useful purposes. Let him constantly apply the princi- 
ple, so tersely expressed by Sir William Hamilton : " The 
primary principle of education is the determination of the 
pupil to self -activity— the doing nothing for him ivhich he 
is able to do for himself This principle is equally ap- 
plicable to every stage of the mind's development, as 
well as to the different processes of instruction adapted 
to these stages ; but it will be impossible accurately 
and effectively to apply it, without a complete knowl- 
edge of the order of mental development, and of the re- 
lation of that development to the study of each of the 
branches prescribed for the instruction and the cultiva- 
tion of the mind. 

Knowledge is to be considered as the food of the 
mind; since by the proper reception, digestion, and 
assimilation of it, the mind is to attain a maturity of 
strength and efficiency; and upon its quality and quan- 
tity it must depend whether that mind is to be healthy 
and vigorous, or puny, sickly, and imbecile. It is, 
therefore, of the greatest importance to ascertain the 



14 INTROD UCTION, 

effect produced upon the mind of the pupil by the 
study of each separate branch of knowledge — what 
faculties it exercises and develops, and what it keeps in 
a state of abeyance or passiveness. The future wants of 
the pupils as to information, must, indeed, be a promi- 
nent consideration in selecting the subjects to be taught ; 
but the teacher should, in the elassilication, as well as 
the instruction, of his pupils constantly keep in view the 
present status of their minds — what they especially need 
in order to acquire vigor, promptitude, and efficiency of 
action. In the first stages of education, the latter 
should be the almost exclusive consideration ; but as 
education advances, the practical usefulness of the 
knowledge imparted should have paramount weight and 
importance. 

The adaptation of the processes of teaching to the 
various subjects taught, as well as to the faculties which 
they call into exercise, should be a prominent object in 
the teacher's mind. Young, untrained, inexperienced 
teachers commit the error of bringing into play, with 
regard to all subjects, association or memory. Tliis, 
with imitation, enables the pupil to present a show of 
knowledge, very gratifying to the unintelligent obser- 
ver, but exceedingly pernicious as a substitute for real 
acquisitions. When a teacher conceives that the sole 
end of his efforts is to enable the pupil to recite verba- 
tim the contents of a particular text-book, or to repeat 
with verbal accuracy and fluency certain rules, defini- 
tions, and formulae, whether their true meaning is 
grasped or not, it is natural that he should resort to the 
shortest and most direct means of accomplishing it, that 
is, constant rote drill — an appeal to the law of arbi- 
trary association. The injury, however, done to the 
mind by this continued process, is incalculable ; since, 



INTRODUCTION. 15 

finally, ideas and facts suggest each other according to 
no intrinsic or philosophical relation, but only from 
their accidental connections, or such as this constant 
repetition may have established ; and thus all logical 
flow of thought is necessarily precluded. 

A determination of what are the best methods of pre- 
senting the subjects to be taught must depend upon the 
relations here referred to. Eules and methods may, in- 
deed, be arbitrarily learned and mechanically applied to 
practice, without any investigation of principles, but no 
such hap-hazard process can, in any case, be sure of 
success ; while in very many it must result in failure. 
This important part of the theory of teaching should 
be carefully studied, not only as preliminary to entering 
upon the di*ties of an instructor, but through every 
stage of their performance. It involves not only a 
knowledge of the laws of mind, but a thorough famil- 
iarity with the subjects taught. "A teacher,^^ says Ed- 
ward Everett, "ought to know of everything much 
more than the learner can be expected to acquire. The 
teacher must know things in a masterly way, curiously, 
nicely, and in their reasons. He must see the truth 
under all its aspects, with its antecedents and conse- 
quents, or he cannot present it in just that shape in 
which the young mind can apprehend it. He must, 
as he holds the diamond up to the sun, turn its facets 
round and round, till the pupil catches its luster.^^ 

A very important inquiry in connection with the right 
manner of presenting the subjects to the pupils' minds, 
is in what manner the subjects sliould be divided into 
topics, and how these topics should be arranged, and in 
what order they should be taken up. The following 
work, embodying, as it does, a graded course of instruc- 
tion, is designed to deal with this inquiry quite exhaust- 



1 6 INTROB TJCTION. 

iyely, and it is in furnishing a guide to the teacher in 
this important part of his duties that its usefulness will 
be found to consist. 

The teacher should study, too, the phenomena of 
morbid as well as of healthy growth ; for teaching, in 
the complete discharge of its functions, has much to do 
in reforming, as well as forming, the mind. While very 
much, in this regard, can be learned only by experience, 
there are many facts and principles already established, 
which the teacher should, as an essential part of his 
professional preparation, acquire. In this connection, 
the automatic tendencies of the mind are to be studied — 
the tendencies, that is, to fall into habits, these when 
depraved constituting what may be called the morbid 
growth of the mind. No part of the teacher's duty is 
more important than the exercise of a constant vigi- 
lance, in order to arrest the formation of deleterious 
habits, or to aid in forming such as are calculated to 
confirm the healthy progress and development of the 
pupil's mind. It is on this account that teachers are 
constantly to be reminded that habits are always more 
valuable than facts — that it is not the quantity of 
knowledge acquired that constitutes a criterion of men- 
tal advancement, but the mode of employing the men- 
tal faculties — the haUts of thought into which the mind 
has settled in making its acquisitions or in applying 
them. In such useful arts as require a mixed exercise 
of the muscular system and the mental faculties, such 
as penmanship, drawing, elocution, etc., this automatic 
tendency has a most important application. Elegant 
hand-writing, distinctness of articulation, correctness 
of intonation, ease and grace of deportment, may all be 
made to rest so firmly on thoroughly fixed habits as to 
become a kind of " second nature." 



INTRODUCTION. 17 

Hoio to use text'ioohs, as well as when and for what 
purposes to employ them, is at the present time particu- 
larly, a most important subject of study to the teacher. 
Though in some branches, and for the attainment of 
certain objects of mental discipline, it is best to dispense 
with them altogether and bring the mind of the teacher 
in direct contact with that of the pupil, yet good -text- 
books must always be among the most important instru- 
mentalities of school instruction, both as regards the 
effect which their judicious use has upon the mind of 
the pupil, and the economy of time and labor of which 
it is the source to the teacher. The latter must have 
learned how to use them aright in order to be successfu.1 
in his work, and the pupil must learn how to make ef- 
fective use of books to be truly educated. 

Most children enter school for the first time with 
minds athirst for knowledge. They have received this 
craving at the hands of Nature, and their whole existence 
has been passed in the effort to satisfy it. By their own 
unaided intelligence they are able to proceed to a certain 
limited extent ; observation is on the alert, and reflection 
begins to be active ; but without the guidance of a ma- 
ture and trained intellect, there can be no method in 
their acquisitions, and the limit of their researches is 
soon reached. The teacher and the book are the instru- 
ments for affording this necessary aid and direction ; but 
in doing this, the tendency should always be to stimu- 
late, not repress, intellectual activity — to bring into 
play the higher faculties of the mind, not to render its 
energies dormant by offering only the dry forms, the 
mouldy skeletons of knowledge, instead of the vital 
germs of intelligence and thought. If, after the various 
grades of school study have been passed, the pupil is 
left with a torpid, vacant mind, the loss which he has 



18 INTRODUCTION. 

sustained is too great to be compensated by even the 
ability to read, write, and cipher. On the other hand, 
a pupil that has not only mastered the elementary prin- 
ciples of science, but has learned how to use books so 
as to supplement the result of his own observations by 
the experience of others, has been more effectually edu- 
cated than he could possibly be by an exclusiye depend- 
ence upon oral instruction. 

One of the most serious abuses to which the employ- 
ment of elementary text-books is liable, is the practice 
of requiring the pupil to commit to memory, verbatim, 
all the definitions of a subject before teaching the subject 
itself, so as to enable the pupils to understand the nature 
of the things defined. It is, of course, most logical in 
the scientific treatment of a subject to place the defini- 
tions first, and the reasoning based upon them afterward, 
but this is not the order of investigation. The defini- 
tions are the results of an induction based upon the 
facts obtained by observation ; they are generalizations 
of those facts, and are unintelligible to those entirely 
unacquainted with the facts themselves. Thus the order 
of investigation is inductive; the treatment is deductive, 
and in elementary teaching the method should conform 
rather to the former than the latter. Give the pupil 
accurate and vivid conceptions of the facts, encourage 
him to observe the phenomena — to collect an experience 
of his own ; tell him, or let him learn from the book 
what has been discovered by the experience of others ; 
and when the facts thus obtained form a sufficient 
ground-work, lead his mind to the proper induction, 
after which the definition, principle, or rule, based upon 
it, comes naturally, and will be thoroughly under- 
stood. The definitions thus taught should be brief and 
accurate in language, and, as a general thing, should be 



INTRODUCTION. 19 

committed to memory verlatim ; for great skill is re- 
quired to construct a good definition, and it is of the 
greatest yalue to the scholar and thinker to have his 
mind well stored with these landmarks and guide-posts 
of knowledge. 

There is a numerous class of subjects in which text- 
books, in the hands of the pupil, are apt to be a bane 
rather than a benefit. The general recognition of this 
fact is quite an interesting feature in the educational 
history of our times. Oljed TeacMng and Oral In- 
structio7i have assumed a prominent place in every ra- 
tional course of study. Both these terms necessarily 
exclude the use of text-books. Teaching from objects 
is merely training the young child to acquire knowledge, 
in a systematic way, from his own experience ; that is, 
by the regular exercise of his obserying faculties. It 
presupposes the presentation of the actual object during 
the*" early stages of the work, so that perceptions may 
pass from it to the mind, and thus ideas be obtained. 
In teaching natural science, at an advanced stage of the 
course, the same method is needed; for it is of very 
little use to attempt to teach facts in relation to the 
phenomena of nature when those phenomena have never 
been observed. It is of no use to talk of the laws of 
light, heat, and electricity — of the movements and ap- 
pearances of the heavenly bodies — or of the chemical 
composition of ordinary substances, as if they were mere 
abstractions. The teacher should never forget that the 
study of the book is the instrument, not the end of in- 
struction; its lifeless representatives of ideas cannot 
dispense with those vivid expressions of thought which 
come fresh from the lips of the teacher. Besides, there 
is a language other than words — a language to which 
the eye, the tones of the voice, the movements of the 



20 INTRODUCTION. 

body, all give force and expressiveness, and added to 
these there is the influence of sympathy, which, though 
a kind of " unconscious tuition," is perhaps the greatest 
element of the teacher's power; and this not alone, or 
chiefly, in intellectual training, but in that which is far 
more important — moral education. The government 
of his pupils — the training of their sensibilities, their 
emotional nature, and their impulses — the instilling of 
right principles of conduct — all these constitute a 
greater part of what may be called a good education, 
than the teaching of the rudiments of knowledge. 
'' Give me the child,'' says Everett, " whose heart has 
embraced without violence the gentle lore of obedience, 
in whom the sprightliness of youth has not encroached 
on deference for authority, and I would rather have him 
for my son, though at the age of twelve he should have 
his alphabet to learn, than be compelled to struggle 
with the caprice of a self-willed, obstinate youth, whose 
bosom has become a viper's nest of unamiable passions, 
although in early attainments he may be the wonder of 
the day." 



Graded Course of Instruction. 



TElNTTH GRADE 

(lowest primahy.) 

Time allowed, about Jive months. 



LANGUAGE. 

JReacZingr.— Words, and wliat they represent ; their sounds, 
and letters ; also short sentences composed of familiar words. 
The alphabet, by review. 

Phonetics. — Simple sounds of letters for training the organs 
of hearing and of speech. 

Spelling,— Words of regular formation — to be taught from 
the blackboard, charts, etc. 



ARITHMETIC. 

Counting and Adding.— Ohiects—SiS balls on the Nu- 
meral Frame, pebbles, etc. 

Figures,— "From to 100, as sjrmbols of the numbers, taught 
by counting objects. 



OBJECT LESSONS. 

Form. — Common shapes, as square, oblong, ball, cylinder, 
cube ; different kinds of corners, and of lines. 



22 GRADED CO UBSE OF INSTR UCTION. 

Color •—Qommon colors, as red, yellow, blue, green, orange, 
purple, to be distinguished. 

Objects. — Names of common objects, their uses, and principal 
parts. 

Human Body.--'FvmQ\^dl parts of the body. 



DRAWING AND WRITING. 

On Slates* — Making dots and small crosses in rows ; draw- 
ing short lines, corners, etc. Printing or writing simple letters. 



MANAGEMENT. 
Length of Exercises. — ^Fifteen minutes at one time. 

DiscixMne, — Constant, but varied employment the best 
means. 



LANGUAGE. 23 

How TO Teach 

SUBJECTS OF THE TENTH (OR LOWEST PRIMARY) GRADE. 



LANGUAGE. 

Meading. — Children learn words as audible signs 
or names of objects, actions, and. qualities, when they 
begin to talk. These words are learned as wholes, at 
once, by hearing them spoken ; not by first learning 
their elementary sounds. In this manner young chil- 
dren gradually become familiar with new words until 
they possess a yocabulary v/hich enables them to make 
known their wants, and to express their thoughts. The 
words which the children thus learn make but little 
impression upon their minds, as tuords, but they are so 
intimately associated with the objects, actions, and 
qualities which they represent that they convey to the 
mind the same ideas as the objects or the actions them- 
selves convey. 

When a child first goes to school it has already learned 
many words, by hearing, as symbols of objects, etc. The 
first duty of the teacher is, to ascertain what words the 
child thus knows, then to teach the young pupil to 
recognize them by their forms. The spoken words are 
first learned as wholes; the printed words should be 
learned first as wholes and associated with both the 
spoken words and the objects which they represent. 

Therefore, teach first short words, which the children 
have learned by hearing ; beginning with the names of 
familiar objects which can be shown to the pupils, or 
the pictures of which may be presented. Also, during 



24 HOW TO TEACH 

the first lesson in reading, print the words on the black- 
board several times, and point them out on charts, etc. 
Let the pupils point out the words on the blackboard, 
and on charts ; also let them print the words on their 
slates. 

Special pains should be taken to lead the children to 
associate the printed words with the objects which they 
represent, either by the use of the objects themselves, 
or by pictures. 

In teaching words that are not names, care should be 
taken to illustrate their meaning by simple phrases, 
conversations, etc. During the earlier lessons, omit 
words of irregular formation, having several silent let- 
ters, such as tongue, Tcnife, hnoio, tliougli, thongJit, etc. 
This class of words may be presented when the pupils 
have learned the alphabet, and its regular combinations, 
and the sounds represented by the letters have been 
taught. 

Let each word be taught first at sight, as a whole, 
and the sounds and names of the letters Which com- 
pose the word be taught afterward. After the chil- 
dren have learned a few words at sight, they may be 
taught the sounds, and the letters which form those 
words. For the purpose of teaching the sound-elements 
of words, select those in which the sounds and letters 
are similar, as cat, rat, hat, mat, ox, fox, lox, etc. The 
teacher should sound the elements or letters of the 
words first, then require the pupils to imitate the 
sounds thus made. But before this can be done suc- 
cessfully the pupils must be trained to disti7iguish, and 
to produce these sounds, as directed under the head of 
Plionetlcs for this grade, which see. As additional 
words are learned, the children may be required to 
name such of the letters as they know, in the new 



LANGUAGE. 25 

words, and then taught the remaining onos in those 
words. In this way let the twenty-six letters of the 
alphabet be taught, progressively. Subsequently these 
should be reviewed, and their usual order learned by 
repetition. The small letters are, of course, tx) be 
taught first. 

After the pupils have learned several single words, 
simple sentences may be presented, as " The dog can 
bark." "The horse can draw a cart." The other 
words that make up these sentences can then be 
learned easily, as parts of the sentence. 

The rapidity with which a child may be taught to 
read by learning to recognize the simple forms of 
words, at first, is surprising. And no less astonishing 
is the readiness with which spelling is afterward 
learned. 

Let the order of teaching reading he, first, the idea; 
then, its sound-symiol, or spoken word ; next, the form- 
symlol, or printed word ; and subsequently, its represeii- 
tation hy writmg ; and the order of learning to read 
the language will correspond with the order of using it. 
Words, then, will become as mirrors, reflecting ob- 
jects and ideas to the minds of the pupils. Sense, and 
soimd, and for77i, and use will become so intimately 
blended together that pupils may easily be led to use 
conversational tones in reading, and a natural style of 
expression will follow as the necessary result. 

But it may be asked. How can the pupils acquire 
the means of learning the new words which they will 
find in reading ? By observing their resemblances to 
words already learned. The child, while learning to 
i*ead, is constantly comparing the forms of new words 
with the forms and sounds of those previously mas- 
tered. The teacher may and should aid the young pupils 
2 



26 HOW TO TEACH 

in acquiring the ability to learn new words by arranging 
in groups, on the blackboard, those already learned, 
and showing them how to compare the forms and 
sounds of these Avords with others. 

For the purpose of leading the children to observe 
readily the analogy of words, in their sounds and in 
the arrangement of their letters, after they have 
learned, objectively and singly, to recognize several 
words at sight, place on the blackboard, in columns, 
such of these words as are similar in spelling and in 
sound, as in the following groups : 



cat, 


pin, 


2)en, 


ox, 


cup, 


rat, 


tin. 


lien, 


fox, 


gun. 


liaty 


• finy 


tenj 


lox, 


run. 


mat. 


in. 


men. 


top. 


fun. 



When the children have learned to pronounce the 
words in a column, at sight, let them learn to give the 
sounds of each, as — t a t , cat ; rat, rat ; liat , hat ; 
etc., not as a spelling exercise, but to impress upon their 
minds the relation of sounds, and of letters as their 
representatives. 

As other words are learned, let new groups be arranged, 
and comparisons made with words of similar form, as : 



old. 


rake, 


me. 


line. 


mule. 


cold. 


make, 


we, 


fine, 


rule, 


told. 


cake. 


see, 


nine. 


cube. 


scold. 


bake* 


bee. 


pine. 


tube. 



If further descriptions of methods for teaching chil- 
dren to read during their first term in school be desired, 
see Suggestions for the Teacher, pages 329-332 of New 
Primary Object Lesso7is. 



LANGUAGE. 27 

Jeffers^s Panoramic Reading Chart will be found ex- 
ceedingly useful during the early lessons in reading, for 
presenting the words objectively. 

Fhonetics. — The object of teaching this subject 
should be, first — to train the organs of hearing^ so that 
the children may readily distinguish the sounds heard 
in speaking our language ; second — to train the organs 
of speech, so that the pupils may learn to produce those 
sounds correctly in using the language. In presenting 
this subject — and this should be done as soon as the 
children begin to learn words by sight — the teacher 
should herself make the sounds, and then require the 
pupils to imitate them, as : a, a ; a, a ; 0,0; 6,6) e,e\ 
e,e\ 1,1; ^, ^ ; u,u; i^,iZ; a, a; a, a; afterward, thus : 
d,d,d, a; e, ^; l,i; 6, 6, q ; u, ii, u. 

When their organs of hearing and of speech have thus 
been trained, both to distinguish and to i7nitate sounds, 
proceed to teach what sounds are represented by the 
letters of simple words, as — in e, mat , cat , man, 
no, not , pin, cup , met, cah e, m ah e, late, 
slate. 

Should more definite directions relative to methods 
for giving the first lessons in Phonetics be desired for 
this and the following grades, see pages 297-308 in 
New Primary Object Lessons. 

Spelling. — After the words have been learned by 
sight and sound, let them be learned by spelling, and 
the children requested to observe that similar spelling 
and similar sounds usually accompany each other. Of 
course many words must be taught simply as signs of 
things, or actions, or qualities, etc., but the plan of 
grouping words by similarity of sounds, as indicated 



28 HOW TO TEACH 

on a preceding page, under the head of Reading, will 
greatly facilitate learning to read, and to spell, also. 

Various modes may be used in teaching the reading 
and the spelling of words singly — for instance: Let the 
pupil point out given words on the blackboard, and on 
the charts, as they are named by the teacher. A word 
may be erased from the blackboard, and the pupils re- 
quested to pronounce the word, and name the letters 
composing it. Parts of words may also be erased, and 
the pupils required to name the missing letters. Let 
the pupils, also, print the words on slates, copying them 
from charts, or the blackboard. 

The list of familiar words taught during the first 
term in school should include those commonly used, as, 
names of articles of dress, food, furniture, and utensils 
used in the house, different things used in the school- 
room, common animals, plants, names of familiar quali- 
ties, actions, etc. 

It is not the small number of letters of which a word 
is formed that renders it easy to be learned objectively, 
but its familiarity by use in conversation. Do not, there- 
fore, confine the pupils to words which are composed of 
only three or four letters. Long, difficult, or anomalous 
words should, however, be omitted in this grade. 

N. B. — In all these exercises of reading and spelling, 
the teacher should — 

Train the pupils to pronounce words readily at sight. 

Never allow them to use unnatural tones in speaking 
or readiiig. 

Correct their faults in the use of language as they 
occur. 



ARITHMETIC, 



29 



ARITHMETIC. 

Counting and Addiitg. — The child's knowl- 
edge of nwnher commences with counting objects. He 
cannot learn the value oi figiii^es from 1 to 10 until he 
can count ten objects. Therefore counting should be 
attended to first. The Numeral Frame is the most 
convenient apparatus to aid in teaching counting, and 
in giving children first ideas of simple numbers. The 
following illustration is intended to represent one mode 
of using the Numeral Frame for teaching counting. 
This mode of using it consists simply in holding the 
Frame before the pu- 
pils, and moving the 
balls on the first wire, 
one at a time, while 
the children count 
" one, two, three, four, 
five, six, seven, eight, 
nine, ten.^' The same 
counting may be re- 
peated on the 'second, 
third, and on each 
succeeding wire. At 
first the counting 
should not extend be- 
yond ten. When all the 

balls on each wire have been counted in this manner, 
proceed to move one tall on each tvire, and let the chil- 
dren count to te7i, as before. Let this exercise be con- 
tinued, from day to day, until each child can count 
from one to ten, alone. Afterward, the counting may be 
extended to ttuenty, by moving the balls on ttuo wires ; 
then to thirty, by moving the balls on three. wires, and 




Counting. 



30 HOW TO TEACH 

SO on to one hundred. When the pupils are allowed to 
count in concert, care should be taken to have them 
use the falling inflection at each number, to prevent 
them from acquiring a sing-song tone. 

Adding. — When the pupils can count to one hun- 
dred by 07ies, the teacher may move two balls at a time, 
and thus train them to add by tivos. As the teacher 
moves two balls on one wire, and two more on the next, 
and so on, the pupils say, " two, four, six, eight, ten, 
twelve, fourteen,'^ etc. 

After the pupils can count, or add thus by tivos^ as 
far as fifty, and have also learned to read and write fig- 
ures as far as 20, the teacher may write a column of 2's 
on the blackboard, and train the pupils to add the fig- 
tires in the same manner as the balls were added. 

Next, the pupils may copy the column of 2's from 
the blackboard, on their slates, and each one add it as 
it was added on the blackboard, and write the sum 
under the column. 

When the pupils have had sufficient practice on a 
column of 2's, both on the blackboard and on their 
slates, to be able to add it readily, the teacher may again 
take the Numeral Frame, move 07ie ball on the first 
wire, and two balls on each succeeding wire, while the 
pupils say, " one, three, five, seven, nine, eleven,^^ etc., 
to fifty-one. When the pupils have learned to add the 
ialls, thus, the teacher may write a column of 2's with 
a 1 under it, on the blackboard, so as to make the 
combinations produce the odd numbers. After suffi- 
cient training upon these combinations, both with the 
Numeral Frame, and the blackboard, require the j)upils 
to Avrite similar columns of 2's with a 1 underneath, 
and add as before, writing the sum below the column. 



ABITHMETIG, 31 

Let the same process be pursued in teaching the ad- 
dition of threes ; first, by balls on the Numeral Frame, 
as three, six, nine, twelve, etc., then by figure 3's on 
the blackboard, and lastly by each pupil's writing the 
figures in columns on the slate, adding them, and 
writing the sum below. Then the threes should be 
combined with one^ next with two^ so as to prodii.ce dif- 
ferent combinations of numbers, as with the twos. 

During a still later stage, the pupils may be taught 
to add by alternating tioos and ones ; then threes and 
ones ; then threes and twos ; then threes, tivos, and 
ones. Each of these steps should be taken first with 
objects^ then 'with figures on the blackboard, and finally 
by the pupils' writing the columns on their slates and 
adding them. The same method may be pursued for 
teaching the addition of fours, fives, and sixes, and 
their combinations with ones, twos, threes, etc., in the 
next or Ninth Grade. The order of the steps is indi- 
cated by the objects employed in teaching, viz. : Num- 
eral Frame, Blackboard, Slates. 

Of course, these exercises with columns of figures 
should not be introduced before the pupils have been 
taught to know figures as symbols, and to make them 
on their slates. 

Value of Ntimbers. — It is exceedingly impor- 
tant that the first ideas of the value of numbers, and of 
figures, be associated with numbers of objects counted. 
Both the vcdiie of nur)ihers and the value of figures 
should be taught in connection with counting objects. 
Here, again, the Numeral Frame is the most useful ap- 
paratus. When the pupils can readily count teji, the 
teacher may hold the Numeral Frame before the class, 
move one ball on the second wire from the top, and 



32 



HOW TO TEACH 



request the pupils to say ^^07ze ball/^ Then the teacher 
may move ttvo balls, one- at a time, on the third wire, 
the pupils counting them as moved, thus : " one, two ; 
two balls/^ Then moye three balls, one at a time, on 
the fourth wire, the pupils counting thus : " one, two, 
three ; three balls/^ Then moYe four balls in the same 
manner ; then Jive balls, and so on. The position of 
the balls on the wire while the pupils are counting, 
may be seen on the sixth wire in the accompanying 

illustration of the 
Vahie of Numiers. 
While the pupils 
are counting "one, 
two, three, four, 
fiye,'^ the teacher 
does not move the 
balls to the side 
of the frame, but 
leaves a space be- 
tween each two 
balls, as may be seen 
in the illustration 
on this page. 

The illustration 
on the next page 
— Simple Vahie of 
Mgures—reipYeseiits 
the teacher in the act of moving the five balls to the side 
of the frame ; and, as he does this, the pupils tell the 
number of balls, thus, " five balls/^ Let the same mode 
be pursued with each number, from one to ni7ie. First, 
the children count the separated balls, as each is moved 
part way; and as all are moved to the side of the 
frame, the pupils tell the whole number of balls moved. 




Value of Numbers. 



ARITHMETIC. 



33 



Next let the pupils tell the number of balls on each 
wire, thus: one ball, two balls, three balls, four balls, 
five balls, six balls, etc., to nine balls ; nine balls, eight 
balls, seven balls, etc., to one ball, no ball. By these 
means the Value of Numiers will be learned thoroughly. 

Figures. — Figures should be introduced as sym- 
bols of the number of objects counted, and presented 
first consecutively, in groups, or steps, as follows: from 
to 9 ; from 10 to 19 ; from 20 to 29 ; from 30 to 39, 
etc. No succeed- 
ing group should 
be presented until 
the preceding one 
has been thorough- 
ly learned, so that 
the pupils can read 
them at sight, in 
order, and out of 
order. While teach- 
ing the Simple 
Value of Figures, 
the Numeral Frame 
will be found a 
most valuable aid. 
During this stage 
of instruction the 

teacher should make frequent use of the blackboard, 
and the pupils of slates. 

Additional suggestions relative to methods for teach- 
ing the First Ideas of Numbers and of Figures, may be 
found on pages 194-209 of New Primary Olject Lessons. 

2* 




Simple Value op Figures. 



34 HOW TO TEACH 



OBJECT LESSONS. . 

]Sr. B. — Each exercise in object lessons should le con- 
ducted loith a vieio to forming habits of attention and 
careful observation through the tcse of the senses. 

Form. — In Nature's school, children first learn to 
know things as wholes ; they learn to know their parts 
afterward. The teacher who would be successful must 
follow Nature's plan of instruction. Present, therefore, 
common objects, as wholes, and lead the pupils to notice 
resemblances in shape, first ; afterward direct their at- 
tention to prominent differences. 

A Box of Forms and Solids^ containing forty-eight 
plane Forms and fifteen Solids, has been prepared for 
the special purpose of Object Teaching. This is the 
most important aid in illustrating the various forms 
and solids. 

Select the Form to be taught from the Box of Forms, 
and lead the pupils to observe it, then tell them its 
name; next require them to mention other objects 
having the same shape. Proceed in this manner with 
each Form and Solid mentioned for this grade, and 
continue these exercises until the pupils can recognize 
and name each. 

Color. — The pupils should be led to distinguish re- 
semblances and differences in color from " colored 
cubes," or cards, and to group together objects of like 
colors. They should also learn the names of the six 
principal colors. 



DRAWING AND WRITING, 35 

Objects. — The lessons on Commo^i Objects in this 
grade should be simple and conyersational, treating 
only of their most obvious parts and uses. Such com- 
mon objects as a bell^ chair, slate, pencil, hat, cup, knife, 
etc., are appropriate for this purpose. The pupils should 
be led to notice and point out the principal parts, and 
encouraged to tell what they see and what they know 
of each object shown them. 

JBTtiman Sody. — In this Grade the lessons on the 
Human Body should lead the pupils to notice and name 
the parts, as head, neck, trunk, arms, hands, legs, feet; 
also parts of the head, as crown, face, forehead, cheeks, 
chin, mouth, nose, eyes, ears, etc. 

N. B. — If more explicit information be desired rela- 
tive to methods for giving lessons on ^Ao^es of lines^ 
corners, square, ohlong, tall, cylinder, cube, and common 
objects ; also on colors, and on the liiiman body, it may 
be found in New Primary Object Lessons. 



DRAWING AND WRITING. 

Dratving on Slates^ etc. — The exercises of 
Draiuing and Printing on slates should be introduced 
in such a manner as to give an interesting variety to 
the class-work ; also, so as to aid in the discipline of 
the class, by giving the children something to do that 
Avill interest them after they have become tired with 
their other lessons. The children might be allowed to 
use slates for drawing, as a reward for good order and 
attention. Short daily exercises may be made very 
useful. 



36 HOW TO TEACH 



MANAGEMENT. 



Ijengfh of Exercises.— The exercises of this 
Grade should not be continued upon the same subject 
longer than fifteen minutes at one time, without mate- 
rially changing the manner of the exercise. 

Discipline.— Yoimg children cannot attend to 
the same thing for a long time without change in the 
form of attention. Their natural activity demands fre- 
quent changes in the position of the body; also con- 
stant but yaried employment. If the teacher does not 
furnish the needed employment and changes of position 
by variety in her methods of instruction, the children 
will seek to gratify their needs by play. Therefore chil- 
dren sJiouId never he compelled to sit witliout employ- 
ment^ eitlier for the mind, the hands, or the lody. 

Children should be led to do right by encouragement 
rather than driven by fear. Judicious praise is more 
efficient than scolding. Teach them to be cleanly, 
mannerly, truthful, and obedient. Let good examples 
of these traits be commended frequently. 



lyTII^TH GEADE. 

(PRIMAKY.) 

Time allowed^ about Jive months. 



LANGUAGE. 

Meading* — In the First Header. 

^Phonetics. — Pupils to be taught to recognize and to make 
the sounds of the letters in words of one syllable. 

De/initions. — Pupils to be practiced in illustrating^ the mean- 
ing of words by their use m short sentences ; also in telling what 
the words mean. 

Spelling^ — Words from the reading lessons; also familiar 
words in common use. 



ARITHMETIC. 

Adding. —With objects, and with figures ; twos, threes, fours, 
and fives. 

Figures.— "Nnmbers of two and of three figures to be read at 
sight, without numeration ; also, to be written on slates from 
dictation. 

Montan Numbers. — I, V, X, L, with theh* combinations 
to sixty, inclusive ; also their use on the face of the clock. 



OBJECT LESSONS. 

Form. — Common shapes, continued ; adding those of rhomb, 
rhomboid, circle, semicircle, crescent, sphere, hemisphere, cone; 
also position of lines. 



38 GBADED CO UBSE OF INSTR UCTION, 

Co^on— Shades of common colors, as light and dark red, 
light and dark blue, etc. 

Human Body. — ISTames and uses of the limbs, and of their 
parts ; also the names and shapes of the principal bones. 

Objects. — The principal parts and chief uses of common 
objects. 



DRAWING AND WRITING. 

On Slates. — Connect dots by lines ; draw squares, oblongs, 
rhombs ; divide lines into equal parts. Write simple words with 
small letters. 



MANAGEMENT. 

Doing. — Train children to see, to do, and to tell. 

Manners and Morals.— JJse the appropriate daily inci- 
dents of school as occasions for giving instruction in Manners 
and Morals. 



LANGUAGE. 39 

How TO TEAOH 

SUBJECTS OF THE NINTH GRADE. 



LANGUAGE. 

Reading. — The manner of teaching Reading dur- 
ing the first term in which books are used by the pupils, 
has a yery important influence on the future progress 
of those pupils. In the processes of instruction, only 
one difficulty should be presented to the puj)ils at a 
time. Among the difficulties which children have to 
encounter during their first lessons in reading from 
books, are, learning to hnoiu tlie words at sights so as to 
pronounce them readily ; learning to hnoio what tlie 
nvords a7id sentences mean ; learning to 7'ead in such a 
mdniier as to iinitate good conversation. 

First Step, — With each new reading lesson the first 
step should be to make the pupils familiar with the 
words of the lesson, by printing them on the blackboard 
in columns, and teaching the children to pronounce 
them at sight; next teach them to pronounce at sight 
the same words in the book, but out of their order in 
the sentences of the lesson, lest they learn them by rote, 
instead of by sight. 

Second Step, — Train the pupils to find out what each 
sentence means, and to tell the meaning in their oiun 
language. 

Third Step, — Train the pupils to read each sentence 
so that the reading may resemble good conversation. 



40^ HOW TO TEACH 

Finally, when the lesson has been read in a proper man- 
ner, the teacher should talk with the children about it, 
and encourage them to tell, in their own language, what 
they have read. 

N. B. — Let the standard for good reading be its near 
resemllance in manner to good conversation. 

Further suggestions relative to first lessons in read- 
ing from books may be found on pages 333-337, of New 
Primary Object Lessons. 

^*^ The work of teaching children to read may be facilitated 
by using, for the First and Second Reading Books, those printed 
with the modified types invented by Dr. Edwin Leigh. 

Phonetics. — The object of exercises in Phonetics 
should be the same in this grade as in the preceding — 
to secure a ready recognition of the several sounds of 
our language, and the ability to utter them distinctly in 
conversation and reading. Time should not be wasted 
in the endeavor to teach children definitions or descrip- 
tions of the various sounds of letters. 

Let the chief aims of the teacher be, to train the 
organs of hearing to acuteness in the perception of 
sounds, and the organs of speech to flexibility and accu- 
racy in producing sounds. 

Definitions. — During the lessons of this grade, it 
is appropriate to teach the children to use the principal 
words of the lesson in brief sentences, to enable them 
to show readily that they understand what the words 
mean, as: ^^A horse can draw a cart,^^ — "I must be 
goodr — ^^I can liold a book.^' — " Snoio is white." — "I 
will try to learn to read." — " I must obey my mother," 



ARITHMETIC. 41 

etc, etc. Such exercises will be found to be much 
more useful to young children than teaching them 
formal definitions to be recited. The meaning of diffi- 
cult or unusual words must, of course, be explained and 
illustrated by the teacher. 

Spelling. — In oral spelling, the words should be 
distinctly pronounced by the pupil before they are 
spelled, then each letter clearly uttered, a pause made 
letiveen the syllailes, and the word again pronounced 
after all the letters have been given. The familiar 
words taught, in addition to those in the reading les- 
sons, should include such appropriate words as the 
children most commonly hear and use. These should 
be printed or written on the blackboard by the teacher, 
and copied by the pupils, on their slates. The same 
words may also be spelled orally. 

The chief use of spelling consists in writing words; 
therefore, as early as possible, it should be taught by 
writing. As the first step in this direction, let pupils 
commence in this grade to study spelling lesso7is iy 
copying the words on slates. 



ARITHMETIC. 

Adding. — It would be well for the teacher, before 
commencing the lessons of this Grade, in Arithmetic, 
to read the directions for teaching "Adding^' in the 
preceding Grade. 

During the exercises of counting and adding with 
the Numeral Frame, do not allow the children to count 
and add by rote. See that due attention is given to 
the objects counted. When the pupils can add readily 



3 


4 


5 


3 


3 


4 


2 


2 


3 


3 


4 


2 


3 


3 


5 


3 


3 


4 


2 


4 


3 


3 


3 


2 


2 


2 


5 


3 


4 


4 



42 ^OTF TO TEACH 

single columns, each composed of like numbers, as all 
2's5 all 3's, 4's, 5's, etc., teach them to add single colunans 
composed of different small numbers, as 2^s and 3's; 
2's, 3's, and 4's ; also 2's, 3's, 4's, and 5's. 
These combinations should be illustrated 
on the Numeral Frame at first, then 
taught with figures on the blackboard ; 
2 and subsequently copied by the pupils on 
their slates, and added by them silently. 
In adding, let the pupils be trained from 
the first to name only the sums, thus : 
3, 5, 8, 10, 13, 15, 18, 20, 23, 25 ;— 4, 6, 
9, 13, 15, 18, 22, 24, 27, 31;— 4, 9, 11, 
14,18,23,25,28,32,37. 
— — — To make the pupils familiar with the 
25 31 37 sums produced by adding the separate 
numbers, 1, 2, 3, 4, 5, 6, 7, 8, 9, to 
each number below 20, arrange the figures on the black- 
board thus : 

12 3 4 5 6 7 8 9 10 11 12 13 14 15 etc. 
1111111111111111 

1 2 3 4 5 6 7 8 9 10 11 12 13 ' 14 15 16 



12 3 4 5 6 7 8 9 10 11 12 13 14 15 

22222222 2 2 2 2 22 2 2 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 



Continue this arrangement until the pupils can add, 
both on the blackboard and on slates, each number 
from 1 to 9 to each number below 20, both in the order 
given, and out of this order. 



ABITHMETia 43 

Reading and Writing Figures. — Both the 
reading and writing of numbers in figures can be 
taught most thoroughly in steps, or groups. The 
figures should be presented first in their order, in con- 
nection with counting; then out of their order. In 
this Grade the figures should be taught loWiout nume- 
ration, 'The following groups will indicate appropriate 
steps : 



First Step. 


Second Step. 


TJiird Step. 


Fourth Step. 


FiftJi Step. 


10 


100 


100 


200 


300 


11 


200 


101 


201 


301 


12 


300 


102 


202 


302 


13 


400 


103 


203 


303 


14 


500 


104 


204 


304 


15 


600 


105 


205 


305 


16 


700 


106 


206 


306 


17 


800 


107 


207 


307 


18 


900. 


108 


. 208 


308 


19 




109 


209 


309 


20 




110 


210 


310 


21 




111 


211 


311 


etc., 




etc., 


etc.. 


etc., 


to 




to 


to 


to. 


99. 




199. 


299. 


399. 



These steps maybe continued in this manner through 
999. As much time will be required to teach the first 
and third steps as for any four other steps. Let the 
children be trained to read and tvrite the numbers con- 
tained in each step, readily, before taking up the next 
one in order. 

If properly conducted, these lessons will train the 
pupils to read and write numbers through 199 in one 
month, and any number expressed by three figures in 
two months. 



44 HOW TO TEACH 

JRoman lumbers. — Besides teaching what num- 
bers are represented by I, V^ X, and L^ and their com- 
binations to sixty, the pupils should be trained to tell 
the time of day as indicated on the face of a clock. 



OBJECT LESSONS. 

FovTn. — ^When the pupils have learned to recognize 
a given shape by means of its representative form in 
the set of " Object Teaching Forms and Solids," they 
should be led to discover the same shape in several 
other objects. See remarks on page 34, relative to 
Form and Methods for teaching it. 

During the first lessons on lines, the attention of the 
pupils was properly directed to their shapes only, as 
straight, crooked, curved, waved, spiral. When they 
are taught to recognize and name ih^ positions of lines, 
as vertical, slanting or oblique, and horizontal, they 
should be trained to apply these names of positions to 
oljeds as well as to lines. 

Color. — In lessons on color, the name should first 
be associated with the color which it represents, by 
showing that color and requiring the pupils to point 
it out on the chart, and among colored objects. To 
recite names and descriptions of colors, without also 
knowing the color when seen, is of no use. The teacher 
should use ^^Color-Cubes," '^Colored-Cards," "Color- 
Charts," and other colored objects for illustrating these 
lessons, and require the pupils to show, by placing in 
groups colors that nearly resemble each other, with 
what degree of accuracy they distinguish colors; and 
at the same time they should be taught to know com- 
mon shades and tints by their names. 



DRAWING AND WRITING. 45 

Stiman Sody. — In giving the lessons on the 
liuman body, let the pupils point out and give the 
names and uses of parts, as parts and uses of the arm, 
hand, leg, foot, etc. 

Objects. — Let the pupils point out parts of objects, 
and the teacher give their names and uses ; then let the 
children give the names and uses of the parts as the 
teacher points to them. 

N. B. — Should the teacher desire more explicit in- 
formation relatiye to methods for giving lessons on 
plane forms, solids, position of lines, shades of colors, 
the liiiman hody, and on common objects, for this and 
the succeeding Grades, than the space will allow in this 
book, it may be found in the treatment of these topics 
in Neiu Primary Object Lessons. 

DRAWING AND WRITING. 

On Slates. — In this Grade, the instruction should 
be continued in a manner similar to that for the Tenth 
Grade, which see. The teacher should give full illus- 
trations on the blackboard, relative to each point and 
step of the lessons. 

MANAGE^IENT. 

Doing. — Childre^i learn much faster by doing than 
by merely repeating what they have been told. There- 
fore, whenever possible, arrange the exercises of each 
subject so that the pupils may be called upon to do 
something which relates to that subject, tuith their 
hands ; also so as to require them to tell what they see 
and do. 



46 HOW TO TEACU, 

Megular Oecupation for all the Pupils. — 

A teacher who furnishes that regular and constant oc- 
cupation which commands the attention of all the pu- 
pils during the several exercises of the day, thereby 
giyes the best assurance of ability to manage a school 
successfully. Indeed, the secret of maintaining good 
discipline chiefly lies in this. Hence the manner of 
teacliing becomes an important element of good man- 
agement as well as of good instruction, for it is this 
which chiefly determines the order of the class. Fur- 
thermore, habits of learning are acquired from the pre- 
yailing methods of teaching. 

To learn how to manage a class or school, so that all 
the pupils may haye constant occupation, and may giye an 
interested attention to all the exercises, should be the 
aim of eyery teacher. Proper changes in the manner 
of presenting the different lessons upon the same subject, 
and eyen changes in the manner of conducting the ex- 
ercise of a single lesson will be useful to the teacher 
toward the attainment of this aim. 

In a class composed of young children, frequent alter- 
nations from answers by indiyidual pupils to responses 
by the entire class will aid in maintaining the attention 
of all the pupils. Great care, howeyer, will be necessary, 
on the part of the teacher, to preyent the pupils, while 
speaking in concert, from using sing-song tones. This 
may be preyented by requiring them always to use the 
falling inflection in answers by the entire class, and by 
neyer allowing them to repeat the answer, or statement, 
without a request from the teacher, made after each re- 
sponse by the class. 



EIGHTH GEADE. 

(primary.) 
Time allowed, — about Jive months. 



LANGUAGE. 

Reading. — First Reader completed, and an easy Second 
Beader commenced ; pupils to be able to read fluently in good 
conversational tones, with proper attention to the pauses. 

I^honetics.Sounds occurring in words of one syllable, and 
silent letters to be distinguished. 

Definitions. — Meaning of the words read to be shown by 
using them in short sentences. 

Spelling. — From reading lessons ; and lists of other familiar 
words. 

ARITHMETIC. 

Adding. — Single columns of ten figures ; adding by decades, 
through ds\ 

Numeration and Notation. — Reading and writing figures 
through nine places (987, 654, 321). 

Mental. — Simple, practical questions which require the add- 
ing of numbers from 5 to 9 to numbers below 30; also, subtract- 
ing similar numbers. . 

Multiplication table commenced. 

Moman Numbers. — Their combinations through two hun- 
dreds. The Key to Roman Numbers to be taught. 



48 GRADED COURSE OF INSTRUCTION, 



OBJECT LESSONS. 

Fovin. — Parallel and perpendicular lines, angles, prisms, 
pyramids, surfaces, circumference, diameter, etc. 

Color. — Primary and secondary colors. 

Suman Body. — Piincipal bones and their uses. 

Animals. — Names and uses of familiar animals ; also where 
they live. 

Plants. — Names of trees, plants, flowers, fmits, etc. ; also 
where they grow. 

Objects. — Pringipal qualities, parts, and uses. 



DRAWING AND WRITING. 

On Slates.— 'Dvdiwmg plane figures ; writing simple words ; 
forrdation of capitals taught. 

MANAGEMENT. 

Physical Training. — Daily physical exercise and pure 
air are indispensable to the health of children. Provide them 
with both during the hours of school duties. 



LAjyaUAGE. 49 



How TO Teaoh 



SUBJECTS OF THE EIGHTH GRADE. 



LANGUAGE. 

Meading. — The exercises for teaching Reading in 
the Eighth Grade may be diyided into thi^ee stejjs^ as in 
the Ninth Grade. 

First Step. — Training the pupils to know the words 
at sight ; also what the words mean. 

Second Step. — Attention to the thoughts expressed. 

Third Step. — Eeading in easy, conversational tones. 

1. The pupils may be trained to know the words at 
sight by writing them in columns on the blackboard — 
by pronouncing them from their books, commencing 
with the last word of the paragraph* and proceeding in 
an order the reverse of that pursued in reading. 

2. As soon as the words are known readily at sight, 
cliief attention sJioiild te given to the thoughts expressed. 
The pupils may be led to attend to the thoughts ex- 
pressed by requiring them to find out what the senten- 
ces tell, without reading them aloud. The teacher may 
aid them in this matter by proceeding in a manner 
similar to the following: Eequest the class to look at 
the first sentence, and each member to raise a hand when 
able to tell what the sentence is about. When se»veral 
hands are held up, call upon different pupils to state, in 
their own language, what the sentence tells. Proceed in 
a similar manner with other sentences of the lesson, and 

3 



oO HOW TO TEACH 

require the pupils to tell what those sentences say. The 
teacher may ask : What does the first line tell us ? 
What do the words in the next sentence say ? Who can 
tell what the next paragraph is about ? 

3. When the pupils haye accomplished the first two 
steps' in a given reading lesson, they will be prepared to 
take the third ste^J, and will readily learn to read with 
easy, conyersational tones. Special care should be taken 
in this grade to train the pupils in habits of clearness 
and distinctness of enunciation, also to read in an easy^ 
speaking voice. 

Faults in reading are most readily overcome when the 
efforts to correct them are chiefly directed to one kind 
at a time, and the training continued until the pupils 
clearly perceive the fault and take the proper means to 
correct it. 

JPunctuation. — The time commonly spent in teach- 
ing children to recite definitions of punctuation-marks 
is wasted. Instead of this, lead the pupils to observe 
that a short jmtise is made at a comma^ a little longer 
pause at a semicolon^ and still longer pauses at the 
question-marJc and period. Lead the pupils to see that 
the question-mark points out a question, and a period 
the end of a sentence. The uses of all the marks of 
pauses, as well as the hyphen, apostrophe, and quota- 
tion-marks, should first be explained from the black- 
board, then examples of their use should be pointed 
out by the pupils in their reading books. 

JPhonetics. — In this grade the pupils should be 
taught to distinguish the sounds of given letters in 
words of one syllable, and to make these sounds, as, the 
sound of a in slate, a in Mil, o in not, o in do, u in full, 



LANGUAGE. 51 

fin far, fin of Tc in TcUbj m in man, c in coto, etc. 
When the pupils can distinguish and make the sounds 
in words of one syllable, they may be required to tell 
which letters have no sound in given words ; also, to 
name the vowel sound by its number ; as in the word 
make, m-a-Tc, make, a has its first sound, the e is silent ; 
'bought, i-a-t, bought ; oit represents the fourth sound of 
a, g and h are silent. 

As a method for training pupils to distinguish the 
silent letters, let them first sound ?i> ^noyA., giving each 
sound as heard when the word is properly pronounced 
— then spell it, naming each letter in order — next tell 
which letters have no sound. 

Care needs to be taken, in each grade, to prevent the 
pupils from making the short sounds of a, e, i, o, and u, 
too long, when sounded alone. Let each of these 
sounds be made very short, as heard in at^ net, it, not, 
nut. 

Definitions* — In giving the nieaning of separate 
words, in some instances a description of the object, or 
of its use, if the word be a name, or a simple statement 
about that which is meant by it, will illustrate the 
pupil's understanding of it better than the use of the 
word in a sentence. Let this exercise be so conducted 
as to avoid mechanical forms of definition, and with a 
sufficient variety and simplicity to secure a clear knowl- 
edge of the meaning of the luords. The practice of 
using the given words in sentences, so as to illustrate 
their meaning, should be continued in this grade. 

Spelling. — Care should be taken in oral spelling to 
have each pupil pronounce the word before spelling it, 
to name each letter distinctly, to make a pause between 



62 HOW TO TEACH 

the syllaUes, and to pronounce the word again when all 
the letters have been named. 

As soon as the pupils can write words on their slates 
they should have much practice in spelling by writing 
words from dictation. 

In selecting familiar words it would be well to re- 
quest the pupils to name words for the teacher to write 
on the blackboard, and all the class, afterward, to copy 
these on their slates. But teachers should not depend 
entirely upon the pupils for such words ; they should add 
to the list other appropriate common words. 



ARITmiETIC. 

Adding. — Continue the exercise of adding single 
columns, in the same manner as in the Ninth Grade, 

making them more 
66778899 difficult, gradually, 
65768798 until the pupils can 
64758697 add readily, without 
63748596 counting, columns 
6 6 7 3 8 4 9 9 of ten or twelve 
65778898 figures each, which 
6 4 7 6 8 7 9 7 are composed of 
6 3 7 5 8 6 9 6 7s, 8s, and 9s. 
66748599 The progressive ar- 
65738498 rangement of these 
64778897 columns is illus- 
63768796 trated here. When 
— — — — — — — — the pupils have 

learned to add a 
column on the blackboard, they should copy it on their 
slates, and then each add it singly, writing the sum 
underneath it. 



AMlTHMETia . 53 

Adding ly Decades will greatly facilitate learning to 
add accurately and rapidly. 

Appropriate* steps toward teaching pupils to add ly 
decades may be taken by writing various combinations 
of numbers on the blackboard, in the following form 
and order, and requiring the pupils to add the numbers 
orally, and afterward to copy them on their slates and 
add them again : 



5 


15 


25 


35 


45 


55 


65 


75 


85 


95 


4 


4 


4 


4 


4 


4 


4 


4 


4 


4 


9 


19 


29 


39 


49 


59 


etc. 








7 


17 


27 


37 


47 


67 


67 


77 


87 


97 


7 


7 


7 


7 


7 


7 


7 


7 


7 


7 


14 


24 


34 


44 


54 


64 


etc. 








9 


19 


29 


39 


49 


59 


69 


79 


89 


99 


7 


7 


7 


7 


7 


7 


7 


7 


7 


7 



16 26 36 46 etc. 

When the various combinations with each of the nine 
digits have been made thus in the form of decades, the 
pupils may be required to review them by writing on 
their slates, in groups, combinations of two numbers 
each, that, when added, will produce in the unit figures 
the following: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. 

By means of these and similar exercises, children 
can be led to observe that the same numbers always 
produce a like figure when added, as that 9 and 7 
always give the unit 6, whether the numbers be 19 
and 7, or 29 and 7, or 37 and 9, or 87 and 9 ; and thus, 
by attending to this fact, while adding single columns, 
they can readily acquire the habit of adding witlioiit 
counting. One of the most eflfectual means toward se- 
curing this habit, in addition to the adding by decades, 



54 EOW TO TEACE 

is to teach the pupils to give special attention to the 
figure representing the units as each successiye number 
is added^ i. e., attention to adding the units. 

To explain this process, the teacher may write a col- 
umn of figures on the blackboai'd, as represented here 

a. h. by the one marked a. Then the pupils may be 

7 — led to notice the unit figure in each case by 

8 — ^^3 the teacher's pointing to the successive num- 

9 — 5 bers to be added, and saying: "8 and 9 

6 — . will give 7 for the unit figure ; 7 and 5 will 

8 — giye 2 ; 2 and 9 will give 1 ; 1 and 9 a ; 5 

7 — 2 and 7 will give 2; 2 and 8 a 0; 6 and 9 a 5; 

5 — 5 and 8 a 3 ; 3 and 7 a 0/' 

9 — During this explanatory process, the 
9 — 1 teacher may write the unit figure opposite 

6 — 2 the number added which produces it, as rep- 
9 — 7 resented in the column marked i. So soon 

8 — as the pupils understand this process of 
— adding and naming the unit figures only, the 
90 teacher should erase the column, h, repre- 
senting these units, and require the pupils to add by 
naming the units, as follows : 8, 7, 2, 1, 0, 5, 2, 0, 6, 5, 
3, 0. When they can do this readily from the black- 
board, the pupils may copy the same column on their 
slates, and add by naming the units in the same manner. 

Then columns made up of other figures may be given 
for similar practice. Afterward the pupils may be 
trained to add by naming the sum, as each number is 
added, as follows: 8, 17, 22, 31, 40, 45, 52, 60, 66,75, 83, 
90. This last form should be followed in the usual 
practice of addition. The preceding ones are intended 
to be used in teaching pupils lioio to add, that they may 
acquire correct habits. 

Teachers may observe that the nuniber of figures in 
the column marked 5, corresponds with the number of 



ARITHMETIC. 55 

tens in the sum of column a — nine — and that 9 tens, 
with the last unit figure, 0, gives the sum of column cl 
But this fact is not of sufficient practical importance to 
render it desirable that much prominence should be 
given to it. 

After pupils have been thoroughly trained in adding 
single columns, and understand Numeration and Nota- 
tion, they can be taught the process of " carrying '^ in 
examples of two or more columns, by a few lessons. 
For teaching the pupils " to carry," at first the examples 
should be very short, consisting of two columns, only. 
Afterward the examples may be made longer, gradually, 
more difficult ones being given by extending both the 
length of the lines and of the columns. Give many 
more examples with a few long columns than with long 
lines. Care should be taken not to embarrass children by 
giving them lo7ig and large examples in addition before 
they can readily add short ones. Let the training be 
thorough in each step, and the progress gradual. The 
work of each succeeding week ought to embrace larger 
examples than were given during the previous one, and 
to furnish sufficient practice to enable the pupils to 
master all the difficulties. 

N^umeration. — On commencing Numeration, the 
three places in the unit's period should be taught by 
the order of their places, and by their names ; as, imifs 
place, the first place on the right-hand side; ten's place, 
the seco)id place from the right-hand side; htmdred's 
place, the third place from the right-hand side. When 
the pupils can name each place at sight, both in order 
and out of order, from the blackboard, and can write 
any number in this period from dictation, proceed to 
teach the thousand's period in a similar manner. The 
places in this period should be taught first as the 



56 HOW TO TEACH 

fourth, fifth, and sixth places ; then the pupils should 
be led to observe the similarity of names between the 
first, second, and third places of the tmifs period, and the 
first, second, and third places of the tliousaiKTs period ; 
as units, tens, hundreds of units ; units, tens, hundreds 
of thousands. When the pupils can both read and 
write any number readily, from units to hundreds of 
thousands, proceed in the same manner to teach the 
million^s period. Train the pupils so that they can 
name any place at sight, in order and out of order, and 
give the order of any place when its name is men- 
tioned ; also write readily any number through hun- 
dreds of millions, from dictation. Care should be taken 
to teach the pupils to write the figures neatly, and in 
straight columns. Two or three weeks may be spent on 
the unit's period, before proceeding to the thousand's 
period. 

Mental Arithmetic. — In the Eighth Grade the 
answers to the questions in Mental Arithmetic should 
be simple and concise. The language used should be 
suflBcient to render the solution of the example, and the 
answer to it, clearly intelligible to a listener, yet so brief 
as not to retard, unnecessarily, the process of mental 
calculation. Appropriate forms for answering questions 
in Mental Arithmetic, in the Eighth Grade, may be seen 
in the following examples : 

How many are six apples and three apples? 
A71S, — Six apples and thi^^^ apples are nine apples. 

If a coat cost $15, and a hat $5, how much will both 
cost ? Ans, — Both Avill cost the sum of $15 and $5, 
which is $20. 

Henry had 8 marbles and bought 4 more ; how many 
marbles had he then ? A71S, — Henry then had the sum 
of 8 marbles and 4 marbles, which is 12 marbles. 



ARITHMETia 57 

A boy had 9 apples and gave away 5 of them ; how 
many apples had he left ? Ans, — He had 4 apples left; 
because, when 5 apples are taken from 9 apples, 4 apples 
will remain. 

Multiplication Table. — In presenting the Mul- 
tiplication Table, it is very desirable that each step be 
thoroughly mastered before taking the succeeding one. 
This table may be illustrated first by means of balls on 
the numeral frame, by arranging the balls in groups of 
tiuos, then of threes. When the groups of hvos have 
been illustrated by the balls, the teacher may write the 
table of twos on the blackboard, thus : 



First Form. 




Second Form. 


First Form. 


2 times 3 are 4 




3x2= 6 


2x3= 6 


3 " 


2 « 6 




6x2=12 


3x3= 9 


4 « 


2 " 8 




9x2=18 


4x3=12 


5 « 


2 «10 




4x2= 8 


5x3=15 


6 " 


2 "12 




7x2=14 


6x3=18 


7 " 


2 «14, 


etc.- 


5x2=10, etc. 


7x3=21, etc, 



On placing the Second Form before the class for the 
first time, the teacher should explain the use of the 
siff7is X and =. The pupils may be told to read the 
sign of multiplication the same as the word " times," 
and the sign of equality the same as " are.^^ 

Let the pupils copy and learn the First Form, so as 
to repeat it, both forward and backward. Afterward 
place the Second Form on the blackboard, and let the 
pupils give each answer orally ; also copy the table and 
write the answers. When the table of tiuos has been 
learned in both forms, teach the table of threes in the 
First Form, then in the Second Form, and afterward 
revietu both of them, in combination, in a Thi^xl Form, 
somewhat as follows : 



58 HOW TO TEACH 

Third For?)!. 

4x2= 8x3= 9x3= 4x3= 

5x3= 5x2= 8x2= 6x3 = 

9x2= 7x3= 2x6= 7x2= 

2x3= 6x2= 3x4= 3x9= 

All the tables may be taught on the same plan— first 
in order, then^ut of order, then by combination with 
the tables previously learned. 'New tables should not 
be presented before the pupils have learned thoroughly 
each preceding one through the three forms. 

Hainan ^mnbers. — In the Eighth Grade, the 
Key to Eoman Numbers should be explained to the 
pupils, and numerous applications of it made to a vari- 
ety of combinations, viz.: When letters representing 
equal values stand side by side, and when a letter rep- 
resenting a smaller number stands on the right-hsLiid 
side of one representing a larger number, the values of 
each are to be added, as II ttuo^ XX tiuentyy VI six, XV 
fifteen, LX sixty, XXX thirty. When the letter repre- 
senting a smaller number stands on the Z^/if-hand side 
of one representing a larger number, the value of the 
Ze/7-hand letter is to be taken from the value of the 
ri^A^-hand letter, as, the value of I is to be taken from 
the value of V in the combination IV, which gives 
four, the number represented by IV ; the value of X 
taken from the value of L in XL gives /orz^y as the 
number represented by XL, etc. Training the pupils 
in numerous applications of this Key will save much of 
the time usually spent in memorizing the Eoman Num- 
bers. It will be well to give unusual combinations, 
occasionally, as— VL; VC; VX; VV; XXXX; LC; 
XLLV ; etc., and request the pupils to apply the Key 
and tell what number each stands for. 



OBJECT LESSONS. 59 



OBJECT LESSONS. 



Form. — Special care should be taken, in teaching 
yarious Forms and Solids, to cause the pupils to dis- 
cover the given shape in other objects than those shown 
by the teacher from the set of " Object-Teaching Forms." 
For the accomplishment of this purpose frequent re- 
views should be had, without presenting the forms which 
represent the shapes that have already been learned, 
when the pupils may be requested to mention several 
objects of the given shapes. 

Lead the pupils to observe that all ijrisms have oblong 
sides, and all pyramids triangular sides; that prisms 
differ in the number of their sides, and in the shape of 
their ends ; that pyramids differ in the number of their 
sides, and in the shape of their bases. 

Lines and Angles, — In teaching pupils what consti- 
tutes parallel lines, lead them to notice the fact that the 
lines are side-by-side ; that they are the same distance 
apart at all opposite points ; afterward, in a subsequent 
grade, they can easily be led to observe that both lines 
extend in the same direction ; also that they can never 
meet. 

In previous grades, the pupils have become familiar 
with the terms sharp, square, and blunt, as applied to 
corners ; use this knowledge to illustrate tlie different 
kinds of angles, and give the terms acute, right, obtuse, 
to be applied to angles, instead of sharp, square, and 
blunt. In explaining the terms relative to lines, angles, 
diameters, etc., each of them should be illustrated on 
the blackboard, and the pupils also required to repre- 
sent them on their slates. 



60 ROW TO TEACH 

Color. — All the lessons on Color should be illus- 
trated with " Color-Charts," " Color-Cubes/' " Colored 
Cards," pieces of ribbon, silk, worsted, or other colored 
objects ; also with good water-colors. Care should be 
taken to make the pupils understand that by mixing 
two Primary colors, a Secondary color will be produced; 
also that no Primary color can be formed by mixing two 
Secondary colors. They should also be taught which 
Primary colors will produce each of the Secondary 
colors ; and what two Primary colors each Secondary 
color contains. 

If desired, more definite directions relative to this 
matter may be found in New Primary Object Lesso7is. 

* Suman Sody. — It is important that the pupils 
should learn to point out the location of those bones 
and other parts of the body for which they are taught 
names and uses. 

Ani'tnals. — The lessons on animals should at first 
be conversational, and of such a character as to lead 
the children to notice, when away from school, the 
various kinds of movements of difierent animals, as, 
walking, running, jumping, hopping, flying, swimming, 
etc. ; so that they may be able to tell what animals 
move in a given manner. 

After the teacher has led the children to observe the 
difierent classes of animals, as beasts, birds, fishes, etc., 
by showing them pictures of each, let them be requested 
to give the names of some animals of each class which 
they have seen. The names thus given might be writ- 
ten on the blackboard in groups corresponding to their 
several classes. 

During these lessons on animals, let the names of 
those used for food, and of their flesh, be written on the 



OBJECT LESSONS. 61 

blackboard as the children mention them, and the 
spelling of each be taught. 

Plants. — After talking with the children about 
different kinds of flowers, plants, grains, fruits, trees, 
etc., which they have seen, and after they are able to 
name several of those most common, their attention 
may be directed to different parts of trees, as, roots, 
trunk, branches, limbs, leaves, etc. The teacher will find 
efficient aid in presenting this subject, by the use of 
"Peai^g's Natural History Series^ for Plants.'^ 

Objects* — Pupils should be led to point out and 
name the parts of common objects, to tell the shape of 
the parts, and the uses, color, etc., of the objects. This 
exercise should be so conducted as to give the children 
the ability to describe readily objects which they see. 

Objects having special qualities in a prominent 
degree should be shown, and the pupils led to observe a 
given quality in several objects, as a means of teaching 
them to recognize the same quality whenever it may 
come within their observation. The spelling of the 
words representing the objects, their parts, uses, color, 
and qualities, may be taught. 

. DRAWING AND WRITING-. 

On Slates. — All necessary explanations and illus- 
trations as to the manner of drawing figures, the foima- 
tion of small letters and capitals, should be made by the 
teacher from the blackboard, first to the whole class ; 
afterward, attention may be directed more to the work 
of individuals of the class, for the purpose of giving 
special instruction. 



e2 DB AWING AND WBITING. 

Let the teacher of the class select, each day, six slates 
from those pupils who have made the most commend- 
able improvement in drawing and writing, and place 
them on her desk for inspection by the class. If prop- 
erly managed, this plan will prove a good incentive to 
improvement in neatness in the drawing and writing. 

Use of Pencils. — The pupils should not be allowed 
to write with short pencils. Particular care must be 
taken as to methods of holding both pencil and pen, 
also to the position of the body while writing and draw- 
ing, to avoid permanent curvature of the spine from 
bending sideways ; and serious injury to the eyesight 
from inclining the head too far forward, and holding it 
too near the desk. 

MANAGEMENT. 

Fhysical Training. — The pupils in all the 
grades should be exercised daily in such a manner as 
to expand the lungs, develop the muscles, and impart 
an easy and graceful carriage to the body. Calisthenic 
exercises may be employed for the attainment of these 
objects. 

Five minutes spent once an hour, or even more fre- 
quently, in simple changes of the position of the body, 
by requiring the school or class to stand and to sit to- 
gether three or four times in succession, also to exercise 
the arms briskly, will do much for the physical comfort 
of pupils, and even increase the progress in their studies. 

The necessity of pure air in a school-room is a matter 
too serious to be neglected by any teacher for a 
single hour. Yet quite too commonly, even where 
the means for securing it have been provided, teachers 
carelessly neglect ventilation. 



SEYElsTTH GEADE. 

(primary.) 
Time allowed^ about five months. 



LANGUAGE. 

Heading. — In a Second B^ader ; with conversational tones — 
the use of Italic letters to be explained. 

JPhonetics. — Sounds of short words in common use to be 
given by the pupils — exercises to be had for correcting indistinct 
enunciation. 

Definitions, — The meaning of words to be given, chiefly by 
their use in short sentences. 

Spelling.— Ovsil and written — words from the reading les- 
sons ; also, other common words. 

ARITHMETIC. 

Addition, — With practical examples. 

Subtraction. — The processes taught and practical examples 
given. 

Multiplication.— M\ilti]^liers from 1 to 12 inclusive. 

Mental Arithmetic. — Practical questions in Addition^ Sub- 
traction, and Multiplication. Also Oral Drills for rapid combina- 
tions of numbers. 

MtUtiplication Ta&?6.— Continued through 12 times 12. 

Monian Numbers. — Reviewed. 

Tables of Measure. — United States money ; time ; liquid 
and dry measures. 



64 GBADED CO UBSE OF INSTR UCTION. 

OBJECT LESSONS. 

Form. — The polygons, arc, radius, and other forms. 

Size, — Comparative, and measured. 

Color. — Harmony of colors. 

Human Body. — Organs of the senses. 

Animals. — Comparison and simple classification by groups, 
families, etc. 

Plants. — Shapes of roots, leaves, flowers, etc. Plants used 
for food, etc. 

Objects and Qualities. — Continued. 

Occupations. — Trades, tools, productions, commodities, etc. 

GEOGRAPHY-PREPARATORY STEPS. 

Place and Directionm — Mrst Position of objects on a 
table. Second. Position of objects in the class-room. Third. 
Location and direction of streets and other objects near the 
school. 

DRAWING AND WRITING. 

On Slates. — Words and short sentences to be written from 
dictation ; Capitals to be used. Drawing simple figures. 

On Paper. — Simple words of small letters. The pupils to 
be taught to write their names, with their ages, and the date. 



LANGUAGE. 65 



How TO Teach 



SUBJECTS OF THE SEVENTH GRADE. 



LANGUAGE. ^ 

Reading. — The methods given for teaching Read- 
ing in the Eighth Grade should be continued in the 
Seventh Grade. It is exceedingly important that chil- 
dren be early trained to give attention to the subject- 
matter of what they read. 

Should the teacher find her class using monotonous 
or unnatural tones, several selections should be made 
of reading lessons that are composed chiefly of conversa- 
tions. These may be used for training the pupils to 
read in easy, speaking tones. Afterwards, other selec- 
tions may follow, and special care be taken to teach the 
pupils to read in a pleasant, colloquial style. Call upon 
different pupils to imitate the style of the best readers 
in the class. 

Two extremes, as to the amount of reading which the 
class is taken over, should be avoided — that of keeping 
the pupils too long on the same lesson, and that of 
reading over many lessons without sufficient attention 
to the matter and manner of reading. The first extreme 
destroys the pupils' interest in this exercise, and pre- 
vents them from acquiring the habit of reading to gain 
information ; the second leads to carelessness in manner, 
and the habit of reading without sufficient attention to 
the subject of the lesson, and to what is related con- 
cerning it. 



66 HOW TO TEACH 

The use of Italics should be illustrated from the black- 
board first, and afterward the pupils should be required 
to find examples in reading lessons, and to tell why the 
given Italic words are used. 

Phonetics. — Care should be taken, in conducting 
the exercises in sounds, to train the pupils in habits of 
distinctness of enunciation, and in the use of smooth 
tones of voice ; — uttering the separated sounds of words 
will aid in accomplishing the first ; and making the 
sounds with varying pitches and dilfferent volumes of 
voice will aid in producing the second. Silent letters 
should be pointed out by the pupils. They should 
also be required to tell what sound each letter has in 
given words, and to make the sound. These sounds 
may be described somewhat as follows: — Call, c has 
the sound of k, a has its fourth sound, the first I 
has its own sound, the second I is silent. Bought, 
1) has its own sound, on represent the fourth sound 
of a, gh are silent, t has its own sound. TMnh, th 
are sounded together, i has its second sound, n has 
the sound of ng, k has its own sound. 

Definitions. — All modes of teaching that will 
allow pupils to give mere memorized definitions, with- 
out the ability to illustrate the meaning of the given 
words by their use in complete sentences should be 
avoided. During the exercises in definitions, the 
pupils' faults of language should be corrected. 

Spelling. — The exercises for teaching spelling in 
the Seventh Grade may be continued as in the Eighth 
Grade. 



ARITHMETIC. 67 



ARITHMETIC. 

Addition. — The exercises in this grade should be 
extended to examples with from four to six columns of 
twelve or fifteen figures each ; and with occasional 
examples of six or eight lines, embracing millions. 
Practical examples, relating to matters of daily occur- 
rence in business, should be given. 

Exercises for training the pupils to add without 
counting should be continued in this grade in a man- 
ner similar to those described for the Eighth Grade, on 
pages 52, 53 and 54. 

Subtraction. — The processes of SiiUraction may 
be arranged in three steps, and taught in their order, 
as follows, viz. : 

First Step. — With short examples in which each figure 
in the subtrahend represents a number that is smaller 
than the one above in the minuend. 

Second Sfe^x — With examples in which it is neces- 
sary to take or " to borrow '' from the column of a 
higher denomination. 

Third StejJ. — With examples having naughts in the 
minuend, making it necessary to take from the third 
or fourth column on the left. 

The Second and Third Ste^JS may be illustrated first 
by the use of bundles of sticks ; also by the use of cents, 
dimes, and dollars, somewhat as follows : From 5 dollars, 
4 dimes, and 2 cents take 2 dollars 8 dimes and 5 cents. 
Since I have only 2 cents, I must take one of the dimes 



68 HOW TO TEACH 

and get it changed into cents. This will leave 3 dimes, 
and give me 12 cents in all. From the 12 cents J can take 
5 cents, and 7 cents will remain. I wish to take 
away 8 dimes, but find that I have only 3 dimes remain- 
ing ; therefore I must take one of the dollars and get 
it changed into dimes, which will leave 4 dollars, and 
give me 13 dimes in all. Now I can take away 8 dimes 
and have 5 dimes left. Then I can take 2 dollars from 
4 dollars, and have 2 dollars left. This explanation 
may be followed by another in which the same figures 
(542 — 285), are used as units, tens, and hundreds* 

The process of representing these illustrations may 
be shown on the blackboard, thus : 

10 10 

4 3 10 4 3 10 

U ^d 2c 0h. ^t. 2 units 

2 8d 5c 2 8 5 



t2 5d 7c 2 5 7 

Afterward the process of the Second and Third Steps 
may be further represented on the blackboard, with 
common examples in subtraction, by cancelling the 
figures from tvhich one has heen taken, and writing the 
remainder above it thus : 

9 9 10 
3 10 5 10 5 10 1 10 3 ^0 10 4 10 

^203 103:^0 2^00^0 
1445 15415 135453 



2818 905 104597 

After this process, commonly called " borrowing ^^ 

(but which is really a change in a part of the higher 

denomination without altering the value of the entire 

number), has been illustrated on the blackboard by the 



ARITHMETIC. 69 

teacher, the pupils should be required to copy on their 
slates the same examples, also the process of tahing 
from a figure representing a number of a higher denom- 
ination, by cancelling \ then similar examples should 
be given them to write out in full, that they may become 
familiar with the process of taking from, by cancelling. 
Forms of illustration for explaining a subject should 
be continued no longer than maybe necessary to enable 
the pupils to understand the subject. The process of 
cancelling in illustrating subtraction should be used for 
a few days only. When it is first dropped, another plan 
may be adopted to represent the changes in the figures. 
A dot may be placed over the figure in the minuend to 
indicate that it must be considered 07ie less in the sub- 
traction, thus : 

42*63 16320 240050 

1445 15415 135453 



2818 905 104597 

In subtracting these examples, the pupil might say : 
3 from 10 leave 7 ; 5 from 14 leave 9 ; 4 from 9 leave 5 ; 
5 from 9 leave 4 ; 3 from 3 leave ; 1 from 2 leaves 1 — 
remainder 104,597. 

This process is shorter and less liable to mistakes in 
practice than the common way of "borrowing one^^ 
from a figure in the minuend, and " carrying one '' to 
the next figure in the subtrahend ; besides, it prepares 
the way for readily understanding the operations in 
^^ Compound Numbers." 

Multiplication. — Instruction in regard to the 
processes of multiplication may be presented in four 
steps, as follows : 



70 HOW TO TEACH 

First Step. — Give examples in which no single prod- 
uct will exceed oiinej as 

243 3,142 3,231 231,232 

2 2 3 3 



486 6,284 9,693 693,696 

Second Step, — Give examples in which it will be neces- 
sary " to carry ^Ho the next column, including multi- 
pliers of a single figure only, from 2 to 5, as : 

345 4,583 2,435 32,563 

2 3 4 5 



690 13,749 9,740 162,815 

Tliird Step. — Give examples, including naughts in the 
multiplicand, and use as multipliers 6, 7, 8 and 9. 

2,034 3,102 14,020 10,050 

6 7 8 9 



12,204 21,714 112,160 90,450 

Fourth Step. — Give examples with multiplicands, as 
in the third step, and use for multipliers 10, 11 and 12. 
Teach the pupils where to write the first figure in each 
partial product. 

24,065 3,108 40,207 

10 11 12 



240,650 3108 80414 

3108 40207 



34,188 482,484 

First, illustrate the step on the blackboard, then give 
the pupils similar examples for practice on their slates. 
When they have become familiar with one step, proceed 
with the next in order. 



ABITHMETia 71 

Mental AritJi^netic— The forms of the answers, 
in this grade, may very properly employ more language 
than in the preceding grade. The following examples 
and solutions of them will represent suitable forms : 

Examples : — A man paid $12 for a barrel of flour, $8 
for a ton of coal, and $5 for a load of wood ; how much 
did he pay for all ? A71S. He paid for all the sum of 
$12, $8, and $5, which is $25. 

A farmer paid $40 for a cow, and sold her for $36; 
how much did he lose ? Ans. He lost the diflerence 
between $36 and $40, which is $4. 

What will 5 oranges cost, at 4 cents each ? A^is. If 
one orange costs 4 cents, 5 oranges will cost 5 times 4 
cents, or 20 cents. 

Oral Drills. — Exercises for the rapid combination of 
numbers should be introduced during this grade, in 
addition to a continuation of drills by the " decades.'^ 

The class may be trained to add seyeral numbers, and 
each pupil to write the result on a slate, or give it 
orally. The teacher may give 7 + 3+4 + 5 + 6 + 4 + 2+4 
+ 5, are how many ? In giving these examples for ad- 
dition, the teacher may say, at first, 7 and 3 and 4 and 
5, etc. Subsequently the pupils should be taught the 
meaning of the word phis, and then these examples 
may be giyen thus : 7 plus 3 plus 4 plus 5, etc. 

Each pupil, having added these numbers mentally, 
should write the sum obtained on the slate, and the 
teacher should then ascertain which pupils have per- 
formed the addition correctly. 

Miiltiplication Tables.— ^hen all of these 
tables, through 12 times 12 have been taught by the 



73 HOW TO TEACH 

three forms as described in the Eighth Grade, they may 
be reviewed from the blackboard in the following form, 
the pupils reading thus : 5 times 6 are 30 ; 6 times 5 
are 30 ; 9 times 5 are 45 ; 5 times 9 are 45, etc. 



5 X 6 are 30 ; 6 x 5 are 30 
9x5 '' 45; 5x9 '* 45 
7x6 " 42; 6x7 " 42 



4 X 8 are 32 ; 8 x 4 are 32. 
6x8 " 8x6 " 

5x8 ** 8x5 " 



4x9 '^ 9x4 " 7x9 " 9x7 *' 

In writing these tables on the blackboard for this 
review, the several products may be omitted, and the 
pupils required to give them from memory. At this 
stage the teacher should explain the use of the sign ( x ) 
of multiplication. 

JRoman Numhers. — Eeview and give further 
applications of the key, as indicated in the directions 
relative to this subject for the Eighth G-rade. 

Tables of Measure. — The tables of weights and 
measures should be introduced first, by talking with 
the pupils about their experience in the use of them, 
and by familiar illustrations given by this means. 
Thus the table of United States money may be illus- 
trated by cents, dimes, and dollars ; that of liquid 
measure, by what the children know about buying milk, 
molasses, kerosene, etc., by the pint and quart ; that of 
dry measure, by purchases at the grocery, by quarts, 
small measures, pecks, etc. ; that of time, by observing 
the hours marked on the clock, a^id by attention to the 
days, weeks, months, etc. 

After talking with the pupils about the uses of a 
given table, write it on the blackboard, and let them 
repeat it ; then they may copy the items on slates, both 



ARITHMETia 



73 



in the order of the table and in a different order. Con- 
tinue the repetition and copying until the table is 
thoroughly learned. Each of the tables may be present- 
ed and learned in a similar manner. 



TABLES FOR THE SEVENTH GRADE. 



United States Money. 



10 mills make 1 cent. 
10 cents *' 1 dime. 
10 dimes " 1 dollar. 
10 dollars " 1 eagle. 



Liquid Measure. 

4 gills make 1 pint. 
2 pints " 1 quart. 
4 quarts ** 1 gallon. 
31i galls. •* 1 barrel. 



100 cents make one dollar. 
50 " " one-half dollar. 
25 " " one quarter of 

a dollar. 
75 cents make three quarters 

of a dollar. 



Dry Measure. 

2 pints make 1 quart. 

2 quarts " 1 small measure. 

8 quarts " 1 peck. 

4 pecks " 1 bushel. 



60 seconds make 
60 minutes " 
24 hours " 
7 days " 

30 or 31 days " 
12 months " 
52 weeks *' 

365 days 

100 years 



Time 

1 minute. 
1 hour. 
1 day. 
1 week. 
1 month. 
1 year. 
1 year 
1 year. 
1 century 



Measure. 

Seasons of the Year. 

Spring, 

Summer, 

Autumn, or Fall, 

Winter. 
March, 

April, \- Are the Spring mos. 
May, 



Da^s of the Week, 

Sunday, 

Monday, 

Tuesday, 

Wednesday, 

Thursday, 

Friday, 

Saturday. 



Are the Summer 
months. 



June, 
July, 
August, 

September, K^^^j^^^^^^^ 
November. [ or Fall months. 
December, ) ^^^ ^^^ ^j^^ 



74 Jiow TO TEACH 

Review. — In reviewing these tables, the teacher may 
question the pnpils somewhat as follows : How many 
hours make a day? How many days make a year? 
How many days make a week ? How many weeks 
make a year? How many minutes make an hour? 
How many months make a year ? What is the shortest 
measure of time ? What does it take to make the long- 
est measure of time ? How many quarts make a gal- 
lon ? How many quarts in three gallons ? How many 
quarts make a peck ? How many pints in two quarts ? 
How many quarts in two pecks ? Which is more, one 
bushel or three pecks ? 

A variety of similar questions may be asked after the 
tables have been learned in their order. 



OBJECT LESSONS. 

It is not intended that each topic under this heading 
shall be made the subject of a lesson each day ; but it 
is expected that a lesson will be given, each day upon 
some one of these topics, and that these shall be varied 
so as to embrace all the topics of the grade during each 
month. Much more time and a greater number of les- 
sons will be required for some of these topics than for 
others. 

Form. — It is very desirable to have the manner of 
presenting the lessons on this subject varied in each 
succeeding grade, so as to avoid the possibility of mem- 
orizing and reciting any formula. To secure this end, 
let the reviews of the matter taug'ht in preceding grades 
be so conducted as to compel attention to the shape of 
the various objects. 



OBJECT LESSONS. 75 

By requiring the pupils to describe the shape of ob- 
jects placed before the class, the teacher will be enabled 
to test their knowledge of for 711, 

Si^e. — This subject may be illustrated by various ob- 
jects, as strings of different sizes and lengths, slips of 
paper of different lengths and widths, and small pieces 
of wood. The pupils will obtain clear perceptions of 
size and of length, by being required to judge of the 
size and length of objects before them, and of lines on 
the blackboard, then to measure these and ascertain 
the approximate correctness of their estimates. Draw- 
ing lines of given lengths on the slate, followed by a 
careful measurement of them, is a valuable means for 
training pupils to accuracy in determining size and 
length by the eye. 

Color.— The lessons on color, for this grade, should 
lead the pupils to perceive that some colors appear well 
when placed side by side, while others do not. For 
this purpose lead them to compare red and gree7i with 
Nue and green ; ilite and orange with yelloio and orange; 
yelloiu and purple with Hue and purple^ or red and 
purple. - 

All lessons on color should be illustrated with colored 
objects. Pieces of ribbon, silk, worsted, colored paper, 
water colors, etc., may be used for this purpose. 

Suman Body. — In teaching children the names 
and uses of the organs of sense, and their parts, special 
effort should be made to lead them to understand the 
subject by means of observations made with their own 
organs of sense. The actual seeing, hearing, feeling, 
tasting, and smelling of objects teach children facts 



76 irOW TO TEACH 

which it is impossible to convey to their minds by- 
means of the memorizing of language, however 
thorough and precise. 

Animals. — The lessons on this subject should lead 
the children to notice the most distinguishing points in 
the structure of animals, and to see how their structure 
is adapted to their liabits of life ; for instance, how .the 
webbed feet of some birds fit them for swimming, and 
how the long legs of others fit them for wading ; how 
the strong claws and strong beaks of some birds enable 
them to feed on flesh ; how the cushion-like feet of the 
cat enable it to walk noiselessly about in search of its 
prey ; how the teeth of the cat and dog are fitted for 
teariug flesh, while those of the rat and squirrelare 
formed for cracking nuts and gnawing hard sub- 
stances. 

The chief aim of these lessons being to train the pu- 
pils in habits of observing nature, so that they may be 
enabled to gain therefrom the most useful knowledge, 
the exercises should be conducted in such a manner as 
to lead them to notice accurately the structure and 
habits of the various animals that come within their 
own observation. The facts thus learned should be, by 
the aid of the teacher, properly classified, as a founda- 
tion for subsequent study of the same subject. 

JPrang^s Natural History Series, with the "Man- 
ual " which accompanies it, will be found a valuable aid 
in giving instruction on Animals and Fla?its. 

Plants. — The lessons on plants, in this grade, may 
appropriately lead the pupils to learn the most common 
shapes of roots, as turnip-shaped, branching, fibrous. 



OBJECT LESSONS. 77' 

conical, tuberous, etc.; also the shapes of leaves, as 
needle-shaped, arrow-shaped, egg-shaped, heart-shaped, 
hand-shaped, etc.; also the common shapes of flower's, 
as funnel-shaped, bell-shaped, pink-shaped, butterfly- 
shaped, helmet shaped, cross-shaped, etc. By suitable 
exercises the teacher should also direct the attention of 
the pupils to plants which are used for food, and lead 
them to observe their mode of growth, form, uses, etc. 

Objects and Qualities^ — Two distinct classes of 
exercises may be given under this heading. One con- 
sists in training the pupils to distinguish given quali- 
ties, by using several objects having the same quality, 
for illustration ; the other, which is more appropriate 
for review exercises, requires the pupils to ascertain 
what qualities a given object possesses. Instruction on 
this subject cannot be considered complete without the 
use of both of these^ classes of exercises, in their proper 
order. 

Observation and Comparison. — Habits of 
observing various objects, and noticing their several 
shapes, colors, qualities and materials of which they are 
made, are exceedingly useful as a means of gaining 
knowledge ; yet habits of comparing two or more ob- 
jects, and observing what qualities, shapes, colors and 
materials they possess in common, constitutes an ad- 
vanced stage of development which not only adds addi- 
tional power of gaining knowledge, but gives to the 
possessor practical ability in whatever sphere of life that 
person may be placed. 

In the preceding grades the pupils have been taught 
to distinguish, and to name the common forms, colors, 



78 HOW TO TEACH 

and most obyious qualities. It is therefore appropriate 
that they now should be trained to discover loMch 
of these forms, colors, and qualities may be found in 
given objects to which their special attention may be 
directed. 

This kind of training sliould be so conducted as to 
develop the individual powers of the pupils. To ac- 
complish this, the teacher must avoid asking such 
questions as might suggest to the pupil what to say, 
rather than leave him to discover the shape, color, qual- 
ity, or material without aid. The teacher should aim 
to train the pupils to discover the principal character- 
istics of an object, instead of telling them what those 
characteristics are, and then asking them questions to 
see if they remember them. 

Steps somewhat like the following are appropriate to 
be taken by the teacher : — 

First. Write on the blackboard the words. Materi- 
als^ Shapes, Colors, Qualities, leaving room to write 
other words under each. Then place some object be- 
fore the pupils, as a common slate, and request them to 
tell what materials, shapes, colors, and qualities they 
observe in it. As these are mentioned by the pupils, 
singly, the teacher may write the word on the black- 
board under its appropriate heading. When the lesson 
is finished, the blackboard will contain something like 
the following : 

Materials. Shajyes. Colors. Qicalities. 

slate, oblong, black. opaque, 

wood, right angles. brittle, 

iron. combustible. 



OBJECT LESSONS. 



79 



Occupations. — The exercises on this topic should 
cause the children to ascertain the names of tools used 
in different occupations, and what is done with these 
tools ; also what articles are made or produced. For 
instance, the teacher might write on the blackboard 
the word carpenter, shoemaker, or painter, and request 
the pupils to ascertain what tools are used by those who 
pursue the given trade, and report on the next day after 
the subject is thus assigned — the teacher writing the 
names of tools mentioned by the pupils on the black- 
board, and the pupils copying them subsequently on 
their slates. These exercises will furnish an excellent 
opportunity for practice in observation, and in describ- 
ing what has been seen. They may be made useful, 
also, for first lessons in composition. 

The form in which these lessons may be placed on 
the blackboard is represented by the following : — 

Name of Occupation. Tools use^d. 

rarnpntpr i ^^^^ Plane, Chisel, Auger, Awl, 
^.arpenter. -j Hammer, Mallet, Rule, Squ 



luare. 



Shoemaker, j^a^t,^;^":.^^^^^^^ 





CABINET-MAKER 




Vools Used. 




Materials. 


Articles Made. 


Saws, 




Black-walnut, ■ 


Tables, 


Planes, 




Mahogany, 


Stands, 


Chisels, 




White Oak, 


Bureaus, 


Bits, 


• 


Cherry, 


Sofas, 


Hand-screws, 


Pine, 


Bedsteads, 


Squares, 




Glue, 


Desks, 


Scrapers, 




Varnish, etc. 


Book-cases, 


Mallet. 






Sideboards. 



80 HOW TO TEACH 



GEOGRAPHY- PREPARATORY STEPS. 

Place and Direction. — The exercises in this 
subject must be objective in their character ; and they 
should be conducted with a yiew to prepare the 
pupils for understanding the elementary steps of Geog- 
raphy. The manner of giving the lessons in steps will 
prove most useful to the pupils. 

First Step, — Train the pupils to observe and de- 
scribe the position of objects on the table in front 
of them, using the terms right, left, front, back, front 
left-hand corner, back right-hand corner, etc. Then 
let the teacher represent the positions of these objects 
on the blackboard. Afterwards request the pupils to 
copy the representation from the blackboard, on their 
slates. 

Second Step, — Train the pupils to notice and describe 
the positions of the parts of the class-room, and of the 
principal articles in it, as : door, windows, blackboard, 
seats, table, chair, closet, etc. 

The teacher should draw the outlines of the class- 
room, and represent the positions of the articles in it, on 
the blackboard, at the same time requiring the pupils 
to tell where to place the representation of each object, 
before drawing it. Subsequently the pupils should 
copy the same on their slates. 

TJiird Step, — Teach the pupils the location of the 
streets near the school, and require them to observe and 
tell in what streets they go while on their way to and 
from school. The terms of direction, as east, west, 
north, south, may be introduced in this step, and the 



DRAWING AND WRITING. 81 

Points of Compass tauglit. Eepresent the locations of 
streets,, buildings near the school, etc., on the black- 
board, and let the pupils copy them, as before. 



DRAWING AND WRITING. 

On Slates. — The lessons in Drawing and Writing 
for this grade, must necessarily be simple, yet they 
should be progressive, and so arranged as to lead to a 
proper training of the eye and hand ; indeed this train- 
ing should be made a prominent object. The black- 
board should be used much in illustrating the exercise^ 
of both drawing and writing. Enlarged copies of good 
drawing cards, also simple drawings from objects may 
be made on the blackboard, and the pupils required to 
copy them on their slates. 

Care should be taken to teach the pupils proper posi- 
tions for sitting, for holding their slates, also for the 
hand and fingers in holding the pen or pencil. 

On Paper. — When writing is commenced with 
ink, do not confine the pupils too long to making the 
simple elements of letters ; let them learn to write 
simple words as soon as practicable. It is not necessary 
that the pupils should write all the lines under each 
copy of a common writing-book. Whenever the pupils 
have made sufficient progress to be able to proceed with 
the next copy in order, let them go on with it. But 
there should be system in the progress ; all the pupils 
in the grade should receive instruction relative to the 
same points, and write the same words simultaneously; 
thus all will attend to the same thing, at the same time, 
and proceed to a new lesson together. Faults in writ- 



S2 HOW TO TEAGK 

ing should be pointed out and illustrated on the black- 
board, and such directions given as will enable the 
pupils to correct those faults. 

Before leaving this grade, the pupils ought to be able 
to write simple words neatly with the pen ; and to 
write their own names, and their age; also the day of 
the month, and the year, in a proper form for dating a 
letter. They should also be able to write familiar 
words, and short sentences from dictation, readily and 
plainly. . 



SIXTH GEADE. 

(highest primary.) 

Time allowed, about fixe inontlis. 



LANGUAGE. 

Heading, — Second Reader completed, or an easy Tliird 
Header commenced; 

JPhonetics. — Words to be analyzed, by sounds ; names of 
the somids to be stated ; faults of enunciation to be cor- 
rected. 

definitions, — The meaning of words to be glyen orally, 
and in writing. 

Spelling. — Words from the reading lessons, also familiar 
words, and short sentences from dictation, both orally, and by 
writing on slates. 

AEITBDIETIO. 
Addition and Siibti^action reviewed, 

3Iiiltiplication continued through multipliers of five figures. 

Division, — Both the long and the short forms. Simple 
practical examples to be given in each of these rules. 

Mental Ainthmetic, — Practical examples in each of the 
fom* simple rules. 

Division Tcible. — Taught in connection with a review of 
the Multiplication Table. 



84 BOW TO TEACH 

Tables of Weight and Measure.— The tables of Com- 
mon or Avoirdupois Weight, of Long, Cloth, and Surface meas- 
ure, also a miscellaneous table to be taught, and those of the 
Seventh Grade to be reviewed. 



OBJECT LESSONS. 

Form. — The shapes of objects to be compared and described, 
and their resemblances and differences stated. 

Muman JBof?i/.— Lessons to be continued as in previous 
grades, and extended. 

Animals. — Comparison and classification continued; also 
size, and where found. 

JPlants. — Parts of leaves; shapes of margins; shapes of 
flowers ; and comparison of members of the same, and of differ- 
ent families of flowers. 

Objects. — Various objects to be examined and their shape, 
color, most obvious qualities, and properties to be stated. The 
distinctions between miner?, vegetable, and animal substances> 
to be taught. 

Occupations. — Exercises to give the pupils habits of observ- 
ing and describing common productions, commodities, etc. ; also 
to give them ideas of the exchange and sale of these. 



GEOGRAPHY. 

First Step. — The location and direction from the school of the 
most prominent objects near the school, and of the places in its 
vicinity. 

Second Step. — Definitions relating to the forms of land and 
water, from cards, blackboard, and outline maps. 



DRAWING AND WRITING, 85 

Third Step, — Teach the name of the city or town, the county, 
and state in which the pupils live, and also of the places in the 
vicinity, showing theii' location on an outline map. 

Fourth Step, — Teach the shape of the Earth by means of a 
globe and hemisphere maps. 

Fifth Step. — Teach the location of the principal countries by 
associations with their most familiar animals, inhabitants, and 
productions ; also the location of the warm and the cold coun- 
tries. 



DRAWING AND WEITING. 

On Slates.— rWnimg to be continued as in the Seventh 
Grade. 

On JPaper. — "Writing in books, from copies, with necessary 
instructions in regard to the position of the body, hand, and 
paper. 



86 HOW TO TEACH 



How TO Teach 



SUBJECTS OF THE SIXTH GBADE. 



LANGUAGE. 

Meading. — Before a new lesson is read, the unfa- 
miliar and difficult words in it should be selected, written 
on the blackboard, carefully pronounced by the teachei^, 
and repeated by the pupils ; also both the meaning and 
the spelling of these words should be taught ; — afterwards 
the teacher should request the pupils to find the same 
words in their reading lessons, and to pronounce "them 
again. 

Occasionally call upon a pupil to read while the other 
members of the class close their books and listen; then, 
at the close of the reading request those who listened 
to state the substance of what was read. This exer- 
cise will train pupils to habits of attentive listening, 
and to a proper regard to the subject-matter. 

In efibrts to correct the faults of a class in reading, 
select first the most common fault, and direct almost 
exclusive attention to that until it is understood and 
easily overcome by the pupils. Then select another 
common fault and proceed in the same manner, giving 
attention to the first one also. Afterward select another 
fault, and proceed in a similar manner, giving attention 
to the three. By this means a class may be trained to 
perceive and overco^ne faults in reading, much more 
effectively than by trying to point out half a dozen 
different kinds of faults at once* 



LANGUAGE. 87 

Phonetics. — The phonic analysis of words should 
train the pupils readily to distinguish and make all the 
sounds in given words^ also to determine which letters 
are silent. It should also lead the pupils to such habits 
of distinctness in articulation as will remove the fault 
of neglecting to sound the final consonants, as d in anc?, 
sencZ; r in far, Q^r\'ing in singi^^^, esitmg, etc.; also 
the errors of sounding improperly, both consonants and 
vowels in the pronunciation of common words. 

No other means is so efficient for training tlie organs 
of speech in clearness and correctness of articulation 
as that of elementary sounds. By suitable exercises 
with these, the ear and the vocal organs may be suc- 
cessfully cultivated, and the means furnished to the 
pupils for determining what are the correct sounds 
of the language, how to produce them, and the ability 
to cultivate their' own organs of speech and tones of 
voice. 

Definitions. — Exercises in which the definitions 
are to be written on slates, in short sentences, should be 
introduced in alternation with oral exercises of a simi- 
lar character. It is desirable that an oral exercise of 
this kind, given as a lesson on one day, should be fol- 
lowed on the next day with the same words to be defined 
in a written exercise, thus training the pupils to write 
as well as to talk. 

In the oral definitions, let the pupils be required to 
tell what given words mean, in their own language, as 
well as to use them in short sentences. One pupil 
may be requested to give a brief definition of a word, 
another pupil to use it in a sentence, and another one 
to illustrate its meaning by describing its use. Habits 



88 HOW TO TEACH 

of reciting formal, memorized definitions would be 
avoided by using thus several modes of giving the mean- 
ing of the same word, and the pupils would learn to 
define, and use words intelligently. 

Spelling. — More attention should be given to writ- 
ten than to oral spelling, in this grade. Words may 
be dictated for the pupils to write on their slates ; short 
sentences may be given for the same purpose; the pu- 
pils may be requested to write the names of classes of 
objects, as names of kinds of food, articles of clothing, 
of furniture, kinds of tools, names of occupations, of 
animals, of trees, of fruits, of articles tbat may be pur- 
chased at a grocery etc., etc. These exercises will enable 
pupils to learn the spelling of a large class of words 
in common use. 



AEITHMETIC. 

Addition and Subtraction. — It is intended that 
the processes of adding and subtracting shall have been 
taught so thoroughly, before the pupils are placed in 
the Sixth Grade, that each one will be able to add and 
subtract with facility, and with a good degree of accu- 
racy. Now, special pains should be taken to teach the 
iises of Addition and Subtraction by means of prac- 
tical examples. A brief review of these rules should 
be had at least once each week, during the entire term 
of the Sixth Grade. 

Multiplicatio7i. — Instruction may be arranged 
and presented in three steps, as follows : 



ARITHMETIC. 89 

Fi7'st Step, — Give examples with mnltipliers of two 
figures only — 13 to 99. 

Second Step. — Give examples with multipliers of three 
figures — 100 to 999 — including some with naughts in 
the multiplicand. 

Third Step. — Give examples with multipliers of four 
or five figures, containing one or more naughts. Both 
the multiplicand and multiplier should be so varied as 
to include all the difficulties arising from the difierent 
positions of naughts. 

Pupils should be carefully trained to write the first 
figure of each partial product in its proper place — under 
the figure used as a multiplier. 

Review each step with practical examples, embracing 
transactions that come within the observation of the 
pupils. 

JDivisiOTl. — This rule can be taught most thor- 
oughly by* commencing the instruction with the " Long 
Division '' form, and using a small number for a divisor. 
Four Steps will indicate the methods and order for 
teaching Division. 

First Step. — Give examples in which each figure of 
the dividend will contain the divisor without a remain- 
der, thus : 

2)486(243 3)963(321 

i_ • ^ 

08 06 

8_ ^ 

06 03 

6 _3 





90 HOW TO TEACH 

Second Stejj. — Give examples with the divisor less 
than te7i, in which remainders will occur during the 
partial divisions, thus : 



4)976(244 


8)9856(1232 


8 


8 


17 


18 


16 


16 


16 


25 


16 


24 





16 




16 







Third Stei^, — Give examples with divisors from 10 to 
15, then teach the " Sliort Division ^^ form ; and subse- 
quently require the pupils to use the Sliort form for 
all examples where the divisor does not exceed 13. 



^540(254 


11) 


1 3564 (324 


15)345(23 


50 




33 


30 


54 




26 


V 45 


50 




22 


45 


40 




44 





40 




44 















In illustrating the Sliort Division form, give the same 
examples, each with only one figure in the divisor, to be 
worked by both the Long and the Sliort forms, taking 
care to arrange the two modes so that the difference 
in their lengths shall readily illustrate why 07ie form 
is called ^^Long Division,^^ and the other one ^^ Short 
Division/^ 

Fourth Step, — Give examples with divisors embracing 
numbers from 15 to 50. Arrange these examples so 



ARITIIMETIG, 91 

that different quotients shall contain naughts in yarious 
positions. Each step should be amply illustrated on 
the blackboard, by the teacher, then a sufficient num- 
ber of examples given to furnish the practice necessary 
to enable the pupils to understand it, before proceeding 
to the succeeding step. 

Teachers should aim first to cause their pupils to un- 
derstand the jjrocesses of the several rules, then to 2ise 
them in an intelligent manner. The object of the drills, 
by means of numerous examples, should be accuracy, 
first; raiyidity, second; never rapidity by neglecting 
accuracy. Practical examples should be given, in each 
of the rules, to insure an understanding of their uses. 

Mektal Arithmetic. — The forms for answering 
questions in addition, subtraction, and multiplication 
in this grade, may be the same as for the Seventh Grade, 
which see. Questions may also be introduced which 
will require both addition and subtraction for their 
solution, as : 

Henry had 18 cents ; he gave two cents for pencils, 
and 6 cents for a sponge ; how many cents had he left ? 
Anstuer. — Henry spent the sum of 2 cents and 6 cents, 
which is 8 cents. He then had left the difference be- 
tween 8 cents and 18 cents, which is 10 cents. 

Division, — How many tops at 3 cents each can be 
bought for 12 cents ? A7is. — As many tops as 3 cents, 
the price of one top, is contained times in 12 cents, 
which is four times ; therefore four tops can be 
bought. 

If 2 apples cost 4 cents, what will one apple cost ? 
jins. — If 2 apples cost 4 cents, one apple will cost one- 
half of four cents, which is two cents. 



92 



HOW TO TEACH 



Division Tables. — The Multiplication Table may 
be so reyiewed as to enable the pupil to learn the Di- 
vision Table easily. The following form will illustrate 
methods for accomplishing this : 



4x7 are 28 ; 4 in 28 seven times. 

7x4" 28; 7 in 28 four " 

6x7 " 42 ; 6 in 42 seven " 

7x6 " 42 ; 7 in 42 six " etc. 



This review, combining Multiplication and Division, 
should be continued through each of the tables; and 
subsequently the teacher may review the Division Tables 
by questions similar to the following: 

How many eights in 32 ? How many sevens in 56 ? 
How many nines in 45 ? How many tiuelves in 108 ? 
How many eights in 96? How many fives in 60? 
How many sixes in 54 ? etc. 

Tables/}/ Weight and 3Ieasure. — The tables 
may be taught as in the Seventh Grade, first, objectively, 
then memorized in order; and all the tables of bofch 
the Seventh and Sixth Grades should be reviewed thor- 
oughly during this grade. 



TABLES FOR THE SIXTH GEADE. 



Common, or Avoirdupois Weight. 

16 ounces make 1 pound. 
8 " " 1 half pound. 

4 " " 1 quarter of a pound 

100 pounds " 1 hundred weight. 
20 hundred weight make 1 ton. 
2000 pounds make 1 ton. 



Long Measthib. 



12 

3 feet 
16^ feet 

5i yards 
40 rods 

8 furlongs 
320 rods 

3 miles 



inches make 1 foot. 
1 yard. 
1 rod. 
1 rod. 
1 furlong. 
1 mile. 
1 mile. 
1 league. 



ABITHMETIG. 



93 



Cloth Measure. 




Surface Measure. 


3 feet make 1 yard. 
36 inches '' 1 " 
18 " " i " 

9 't '* J " 


144 square inches make 1 square foot. 
9 '' feet '^ 1 " yard. 
30i " yards "1 " rod. 
160 " rods " lacre. 


4i " " i " 


640 acres 


" 1 square mile. 


4 quarters " 1 ** 








Miscellaneous Table. 




12 things make 1 dozen. 
144 . " "1 gi'oss. 
12 dozen " 1 " 


48 pounds make 1 bushel of barley, 
[or buckwheat. 
58 " " 1 bushel of corn. 


12 gross " 1 great gross. 
20 things " 1 score. 


60 
196 




1 '^ " wheat. 
1 barrel of flour. 


24 sheets " 1 quire of paper. 

20 quu-es " 1 ream. 

32 pounds " 1 bushel of oats. 


200 
280 


(< u 
;( (( 


1 '' " pork, 
[beef, or fish. 
1 " of salt. 



Revieiv. — After these tables have been thoroughly 
learned in order, the teacher may conduct brief reviews 
of those of both the Seyenth and Sixth Grades, by 
questions somewhat like the following : 

How many inches in three-quarters of a yard ? How 
many yards in one rod ? How many rods in a mile ? 
How many square inches in a square foot ? How many 
buttons in a gross ? How many sheets of paper in a 
quire ? How many in half of a quire ? How many 
pounds in a barrel of flour ? Which is heavier, a bushel 
of wheat or a bushel of corn ? How many pounds in 
half of a ton ? How many pecks in two bushels ? 
How many quarts in two gallons ? How many days 
in a year ? How many months in half of a year ? How 
many square feet in a square yard ? Which is longer, 
six feet or two yards ? 



94 HOW TO TEACH 



OBJECT LESSONS. 

The yarious topics embraced in Object Lessons furnish 
far more effectiye means for thoroughly developing th-e 
minds of children than any exercises that pertain ex- 
clusively to reading, spelling, arithmetic, etc. Ciiildren 
whose powers of mind have been developed by proper 
training, so that they observe, compare, classify, and 
describe intelligently whatever comes within the range 
of their observation, will learn every subject more easily 
than they could have done without such training. For 
these reasons suitable attention should be given in each 
grade, to all the topics embraced under the head of 
Object Lessons. And teachers should keep promi- 
nently in view the importance of these lessons as a 
means for proper mental discipline, and not regard the 
knowledge gained by the exercises as comprising their 
chief value. 

Due attention to these considerations will lead teach- 
ers to regard, as of much importance, the manner of 
givi7ig the lesson. 

Form. — The character of the instruction in this 
subject, especially so far as it pertains to learning to 
recognize and describe the various /orT??^^ and solids, need 
not differ materially in the Seventh and Sixth Grades. 
However, when the several shapes required have been 
learned by means of the regular forms and solids pro- 
vided for this purpose, the time given to this topic should 
be chiefly devoted to comparing and describing other 
objects by their shape, stating wherein those compared 
resemble each other, and wherein they differ. 



OBJECT LESSONS. 95 

Huifian Body. — The lessons in this grade should 
be conducted so as to review the facts learned in pre- 
vious grades, and also so as to extend the pupils^ knowl- 
edge of the laws of health, especially so far as these 
pertain to the condition of the skin, habits of cleanli- 
ness, and the manner of eating. 

Animal,s. — The manner of conducting the lessons 
on this topic for the Sixth Grade classes may be^nearly 
the same as that for the Seventh Grade ; but the pupils 
in this grade should be led to consider a greater num- 
ber of animals than those in the previous one, and to ob- 
serve more carefully the peculiarities of structure, etc., 
with a view to extending their knowledge of classifi- 
cation. 

To aid the pupils in making groups of animals, by 
simple classification, let the teacher write on the black- 
. board the following and similar names for groups: 

Swimming BirdSy Cud-cheiuing Quadrupeds^ 

Wading Birds, Flesh-eating Quadruj^eds, 

Climbing Birds, Gnawing Quadriii^eds, 

Scratcliing Birds, Insects, 

Flesh-eating Birds, Reptiles, 

Perching Birds. Fish. 

Then request the pupils to give the names of animals 
to be written under each heading. 

These lessons relative to animals should lead the 
children to make comparisons as to form, structure, 
habits, size, etc., and to learn in what countries and 
localities the various birds and quadrupeds may be 
found. 

Prakg's Natural History Series will be found 
adapted to giving this instruction. 



96 HOW TO TEACH 

Flants. — The lessons on this subject in the Sixth 
Grade may lead the pupils to consider the parts and 
uses of leaves, their margins, parts and uses of flowers, 
as petals, stamens, pistil, etc. ; the comparison of pinks, 
lilies, fruit-blossoms, etc., with a view to noticing re- 
semblances in those of the same family, and differences 
in others; also kinds of fruits which the pupils have 
seen — the names to be written on the blackboard, and 
copied by the pupils on their slates, as a spelling exer- 
cise. The names of fruits and grasses used for food, 
etc., may be written in groups. Like the lessons on 
animals, these exercises should be so conducted as to 
lead the pupils to form habits of carefully studying na- 
ture, as a means of pleasure and as a source of knowl- 
edge; therefore, the time selected for giving the lessons 
on plants, etc., should be during the seasons when the 
pupils can personally examine these objects. 

The teacher would do well to consult two excellent 
works by Prof. Gray — How Plants Groio ; and How 
Plants Behave. 



Objects. — In the Sixth Grade the lessons on objects 
should include their descriptions as to form, color, and 
most obvious qualities. In this connection, it is desir- 
able that the pupils be led to consider what qualities 
are necessary in the substances used for various tools, 
utensils, articles of dress, etc. For instance, what qual- 
ity is necessary for w^agon and other springs ? What 
qualities make sponge useful ? What qualities render 
salt and sugar valuable ? What qualities give value to 
India rubber ? What qualities give value to glass ? 
What to steel ? to iron ? Why will not lead make 
good springs, or knives ? 



OBJECT LESSONS. 9 7 

The lessons under this topic should cause the pupils 
to consider wherein animals, vegetables, and minerals 
differ from each other. Pupils will understand this 
subject more thoroughly by presenting the instruction 
in three steps. 

First Step, — Eequest the pupils to obserye slate-pen- 
cils, pieces of stone, iron, lead, chalk, and various pieces 
of wood, small plants, etc., and then to tell what can be 
done with the wood and plants, that cannot be done 
with stone, iron, etc. Also lead them to consider- whether 
both of these classes of substances are obtained from 
the same source, and whether the iron and stone grow 
as the wood and small plants do. When the most ob- 
vious differences between these two classes of substan- 
ces have been perceived by the pupils, give the term 
Mineral as the name for one class? and Vegetable as the 
name for the other. 

Second Step. — The teacher may next call attention to 
the three great classes of substances — mineral, vegeta- 
ble, and animal — and lead the pupils to observe, and to 
tell what animals and vegetables can do (as take food, 
breathe, grow, die), which minerals cannot do. 

Third Step. — Let the pupils be led to notice what 
animals generally can do .which vegetables generally can- 
not do (as move from place to place by their own pow- 
er) ; also to observe the differences between the food of 
plants and that of animals ; as that plants feed on min- 
erals, or simple substances from the earth and air, while 
animals feed on vegetables and other animals. 

The pupils might also be taught that substances 
which once formed a part of an animal, as wool, hair, 
bone, skin, are called a'tiimal siil stances ; that wood, 

5 



98 HOW TO TEACH 

bark^ gum, sugar, that once formed a part of a yegeta* 
ble, are called vegetable substances. 

Occupations. — The exercises on this topic should 
not only lead the pupils to observe and describe com- 
mon productions, and manufactured articles, but should 
also lead them to consider the necessity for buying and 
selling productions and articles of manufacture ; also 
how these are taken from those who raise or make them 
to those who want to use them. 



GEOGRAPHY. 

First Step, — Review the Points of Compass^ in train- 
ing the pupils, until they are able to name any direc- 
tion, as the teacher points, and to point in any direction 
named. 

In connection with and following the instruction 
relative to the points of compass, lead the pupils to 
learn the location, and the direction from the school of 
other streets near the school ; also of prominent build- 
ings, as churches, post-office, hotel, railroad depot, 
etc. ; or of villages, lakes, farms, groves, forest, streams, 
etc., within the range of the children's observation. 
The teacher should represent on the blackboard the 
situation of the school-house, and the location and direc- 
tion from it of the places mentioned, and allow the 
pupils to copy the same on their slates. 

Second Step. — While teaching the definitions relative 
to t\ie forms of land and water, present first the picture, 
or a drawing upon the blackboard, of the object under 
consideration, as of an island, peninsula, cape, strait, 



GEOGRAPHY, 99 

lake, bay, riyer, etc. ; then show how the same or a 
similar object is represented on a map. Follow this 
with a definition to be learned by the pupils. As the 
characteristics of each form of land or water — as that 
an island is land entirely surrounded hy ivater — is 
learned, require the pupils to point out on a map several 
representations of islands, omitting the names of the 
particular islands in this stage. Proceed in a similar 
way to teach all the definitions. 

Colton's Geographical Cards will be found of great 
assistance as pictorial and map representations to illus- 
trate these definitions. 

During this step the instruction has for its chief 
object training children to recognize the various forms 
of land and water, by means of their characteristic 
features, and to describe each by suitable definitions ; 
hence the attention of pupils need not be directed to 
the names and location of particular islands, isthmuses, 
straits, bays, etc., at this time. 

Third Step. — Commence the instruction relative to 
the names and location of particular places with the 
town, village, or city in which the school is situated, 
and extend it to other places in its vicinity. No fixed 
limit to the extent of this exercise can be given, since 
the length to which it can be profitably carried will 
depend, in some degree, upon the personal knowledge 
of the members of the class relative to these places. 
The teacher should aim, however, so to use the knowl- 
edge of those pupils whose personal visitations have 
made them acquainted with the locations of the great- 
est number of places, as to extend the knowledge of 
the other pupils. 



100 sow TO TEACH 

Such attention should be given to the location upon 
a map of the town, village, or city in which the school 
is situated, and to the relative location and direction 
from it of the chief places in its vicinity, that the 
pupils will be able to point them out on an outline 
map. The name of the* town, village, or city, of the 
county, and of the State in which the pupils live, should 
be taught, and their location shown on a map. 

Fourth Step. — In teaching the shape of the earth by 
means of a globe, lead the pupils to compare a marble 
with an orange, and both the marble and orange with 
a globe, and thus to notice that each one resembles the 
other in shape only ; also that each diflPers from the 
other in size. By this means prepare them for under- 
standing that the globe represents the earth only in 
shape. Follow this with some simple illustrations as to 
the comparative size of the earth. 

Next lead the pupils to compare the outline forms of 
the grand divisions of land, water, and of islands, etc., 
represented on the globe, with their corresponding repre- 
sentations upon hemisphere maps. 

' Fifth Step. — Talk with the pupils about people of 
different races and nations, and point out on the globe, 
also on outline maps, the location of the countries where 
each may be found : as Africa, the home of the colored 
men; China, the home of the Chinamen ; Germany, the 
home of Germans, etc. Proceed in a similar manner 
with the most familiar animals, and the most common 
productions of different countries. Give the name of 
the country, and show its location on a globe, also on 
an outline map. Point out Greenland as the home of 
the white bear; Africa as the home of the lion, zebra, 



GEOGRAPET. 101 

ostrich and camel ; Australia as the home of the kan- 
garoo; Spain as the country where cork and raisins are 
produced ; South America as the country from which 
brazil-nuts and cocoa-nuts are obtained ; West Indies 
as the place from whence we obtain oranges and bana- 
nas, etc. 

By means similar to that herein described the pupils 
may be made to realize that Geography teaches them 
about the homes of the different people, animals, and 
productions which they have seen, and of which they 
have heard. 

The aim of the teacher should be to give the pupils a 
good, general idea of the shape of the Earthy of the 
different portions of it as the homes of races of men^ 
also as the places where particular fruits grow ; and of 
some parts as having continuous cold weather, and 
others continuous warm weather. This object must be 
accomplished chiefly by oral instruction. However, the 
work may be facilitated by placing in the hands of the 
pupils suitable text-books on Geography, to be exam- 
ined by the children after the lesson has been given 
orally by the teacher ; but in no case should the pupils 
in this grade ie required to study a lesson in the hooh 
before the suiject of it has ieen presented orally by the 
teacher, as above indicated. 

Each lesson may be gone over a second time by the 
teacher, after the pupils have studied the subject in 
their books. The order of the lessons, the topics pre- 
sented, and the general character of the facts taught 
should conform to the directions given here, without 
regard to the order of presentation in the text-books in 
common use. 

After completing the course of objective instruction 
in Geography, as indicated in the preceding steps, the 



102 ^OW TO TEACH. 

pupils will be prepared to commence the study of this 
subject in an intelligent manner from good text- 
books. 

DRAWING AND WRITING. 

The exercises in Drawing and Writing for the Sixth 
Grade may be continued in a manner similar to those 
of the Seventh Grade. Pupils should not be simply 
allowed to write, they should be taught and trai?ied Jioiu 
to write by the teacher. Children need something 
besides copy-books, to become good writers. 



GENERAL SUGGESTIONS. 

JRevieivs. — Such a review of the previous lesson, as 
an introduction to, and in connection with, each new les- 
son of the same subject, should be had as will cause the 
pupils properly to associate together the important facts 
previously learned with those of the new lesson. 

General reviews of subjects should be had at least 
once during each month. On these occasions the lead- 
ing facts learned in previous grades, upon that subject, 
should be included. These remarks are intended espe- 
cially for the first five grades of this course of instruc- 
tion. 

Progress of Classes. — Whenever it is found that 
a class has advanced further in one or two subjects of its 
grade than it has in others, the teacher should devote 
less time to the subject in which the class has thus 
advanced, and give more time to the subjects in which 
the class has made the least progress. By this means 
the grade of the class may be equalized in all its studies. 



GENERAL SUGGESTIONS. 103 

No study of a succeeding grade should be introduced 
into a class of a lower grade before that class has com- 
pleted the requirements of the grade in all its studies. 

Ti^ne Given to Each Subject.— The pupils 
belonging to the first five grades of this course should 
not spend more than forty minutes, at one time, upon 
the same subject. And in the first two grades they 
should not spend more than twenty minutes upon the 
same subject at one time. 

The mind, as well as the body, needs rest Both a 
change of subject, and a change in the manner of con- 
ducting class exercises, are necessary to furnish the 
opportunities for needed rest during school hours, be- 
sides the usual recesses of school. 

Vocal il!fi/:8ic,— Instruction in vocal music ought to 
be given to the pupils of all the grades in every school. 

Principles of Education Applied. — Teach- 
ers who learn to apply principles of Education in the 
order of presenting knowledge, and in their methods of 
teaching, will rarely fail of becoming successful in their 
work. They will early acquire the ability to determine 
for themselves how to commence the instruction of any 
class under any conditions, and to proceed surely step 
by step toward the end in view. The following hints 
are given as suggestions to young teachers who desire 
to attain this ability. 

Principle. — Commence instruction in each subject 
with that which the pupils already know concerning it, 
or with something known which is nearly related to it, 
and proceed to the kindred unknown which forms the 
subject of the lessom 



104 • HOW TO TEACH. 

To ascertain the known, or the related unknown, the 
teacher must consider what previous opportunities the 
children have had for obtaining knowledge of the sub- 
ject, and then by questions determine the true attain- 
ments of the pupils relative to the matter for the pro- 
posed lesson. The next point for the teacher to decide 
is, how can that which the pupils already know, con- 
cerning the subject of the lesson, be used in the best 
manner to aid them in learning that which they do not 
yet know of it. For illustration, let this principle be ap- 
plied to teaching Reading to a class of young children 
that have just commenced going to school. 

What is the known to these children, which relates 
to reading ? [See page 23.] 

What is the unknown to be first taught as reading ? 
[See page 23.] 

How can the known be used to aid in teaching the 
unknown, which should form the lesson for this stage 
of the instruction ? [See pages 23, 24, 25.] 

Suppose a class has made sufficient progress in learning 
to read to be ready to commence using the first reading 
book. What then would constitute the unknown which 
should be taught first? [See page 39.] 

How, subsequently, may the known be used for teach- 
ing that unknown which forms the main object of the 
lesson ? [See pages 39, 40.] 

After this manner the subjects of instruction should 
be examined by the teacher, in each of the grades; 
and, as a most important part of the process of teach- 
ing, the main points of each preceding lesson should 
be reviewed, before proceeding with the new matter, as 
a means of connecting the instruction of successive 
lessons so as to make the knowledge acquired a complete 
whole, so far as it extends. 



FIFTH GRADE 

(lowest grammar school.) 

Time allowed^ about jive Tnonths, 

OUTLINE COURSE. 



LANGUAGE. 

Heading. — Of the grade of a Third Reader (first half), with 
a review of punctuation, Roman numbers, and elementary 
sounds; and with exercises on the subject-matter of the les- 
sons. 

Spelling. — From the reading lessons, with miscellaneous 
words, and words derived therefrom ; also exercises in writing 
words and short sentences from dictation. Particular attention 
to be given to the use of capitals. 

Definitions. — From the reading lessons, to teach the mean- 
ing of the words, with illustrations by forming sentences ; in no 
case to be committed to memory and mechanically recited. 

Orammar. — Correction of Language, 



AEITHlIETia 

Mental Arithtnetic. — As far as in written arithmetic, to 
include exercises in the analysis of operations and examples, 
and in rapid calculation without analysis. 

Written Arithmetic. — Through the simple rules and Fede- 
ral money, with practical examples. 

Tables of weights, measures, etc, completed and reviewed, 
with practical illustrations and simple applications. 

5* 



106 HOW TO TEACH 



GEOGRAPHY. 

First Stage. — Simplest elementary and systematic general out- 
line of the geography of the world as a whole, with definitions 
and illustrations by means of the globe, of the form, magnitude, 
motions of the earth, zones, latitude, longitude, etc. 

Second Stage. — Outlines of North America and the West In- 
dies, including local and descriptive geography. 



ELEMENTARY SCIENCE. 

Foodf Clothing^ and Building Materials—Zoology . 

— By oral instruction, to develop the powers of observation and 
reflection, and to cultivate facility in oral description. • 



DRAWING AND WRITING. 

On Slates. — Continued. 

On Paper.— WrWing in books, with particular attention to 
position, holding pen, etc., etc., as in Sixth Grade. 

1. Words containing easy combinations; as man, name, 
noon, soon, etc. 

2. Words containing long and short letters ; as heart, long^ 
youth, etc. 

3. Words with easy capitals ; as Ape, Cold, Ink, Lamb, TimCy 
Useful, Vanquish^ etc. 



LANQUAOE. 107 



How TO Teach 



SUBJECTS OF THE PIFTH GRADE. 



LANGUAGE. 

Meuding. — In teaching reading in this grade and 
in the two or three others immediately succeeding, the 
chief difficulties to be overcome may be classed under 
the following heads : 

First — Hesitation over, or tJie miscaTliiig of familiar 
words. 

This arises from want of practice, and where strongly 
marked should claim the chief attention. 

Second. — Mispronunciation of recognized words, as 
stu7i for st07iey wi7ider for window^ theater for theatery 
etc. 

Third. — New ivords oi ^\iic\i the meaning and pro- 
nunciation are not yet known to the pupil. 

New and difficult words should be carefully pro- 
nounced, and, if necessary, explained, before the piece 
or paragraph is read by the pupils. 

Fourth. — Faulty enunciation. This is in great part 
a physical difficulty arising from deficient training of 
the Yocal organs and of the ear, though sometimes the 
result of slight malformation. 

Distinctness of articulation and the avoidance of all 
improper clipping of terminations, and of the omission 



108 HOW TO TEACH 

or slurring of syllables, should receive careful and con- 
stant attention. 

Lists of common words liable to be mispronounced, 
such as length and strength^ should be made by the 
teacher, and the class exercised upon them. The ele- 
mentary sounds and their m,ore difficult combinations 
in words and phrases requiring great mobility of the 
vocal organs, and especially ^/^aZ consonants, should re- 
ceive frequent attention. It should not be forgotten that 
the difficulty here is chiefly physical, and can be readily 
overcome by suitable exercises. To show a class the im- 
portance of mobility of the muscles of the lips, let the 
teacher read a paragraph with the lips almost motion- 
less, and then read it again, giving as much play as pos- 
sible to these muscles. The great contrast in distinct- 
ness of articulation will be at once manifest. Among 
the best exercises for the purpose of improving the 
enunciation are the well-known "Three gray geese and 
three gray ganders," "She sells sea-shells." "Saw six 
slim saplings," " Peter Piper," " Theophilus Thistle," 
"Amidst the mists," etc., etc. A daily exercise of five 
minutes would probably be sufficient in most cases. It 
should be very spirited,4he shorter sentences twice or 
thrice repeated, and with the greatest rapidity consist- 
ent with perfect distinctness. 

Particular attention s,hould be given to pupils of for- 
eign birth or parentage, so as to insure their mastery 
of the principal difficulties of English pronunciation. 
Phonetic drills are very useful for this purpose. 

Fifth. — Harsh or unnatural tones. The voice and 
manner of the pupil should accord with the character 
and sentiment of the selection. All drawling, sing-song 
tones should be prevented. This is easily done when 



LANGUAGE, 109 

the pupils are led to understand and enter into the spirit 
of the piece. 

In the employment of concert exercises in reading, 
especial care should be taken to prevent any injury to 
the voice by harsh or unnatural tones. 

Sixth, — Vague or erroneous conception oi the subject- 
matter of the lesson as a whole, or of the meaning of 
particular phrases, sentences, or paragraphs. 

When the character of the paragraph or of the les- 
son will permit it, the pupils should be ^ accustomed to 
state, in their own language, the important facts, prin- 
ciples, and moral lessons therein taught. Words, phrases, 
or allusions should be briefly explained, whenever neces- 
sary for the proper understanding of the piece read. 

Seventh. — Want of rhetorical training. Should a 
large number of consecutive lessons in the Eeader be 
of the same general character, a part should be omitted, 
so as to give variety of style and subject. No selec- 
tion, other than the best English poetry, should be so 
long dwelt upon and so frequently repeated as to ren- 
der the exercise a mere recitation. 

As a test of the general condition of the reading, 
classes should occasionally be called upon to read un- 
familiar pieces of the same grade. 

Where the primary object of the exercise is to teach 
elocution, it is advisable, quite often, to require all the 
pupils, except thd one reading, to close their books, the 
teacher also, only using the book for occasional refer- 
ence. In this way, both the teacher and the class will 
be better able to criticise, and the criticism will be more 
just and valuable. Besides, the pupils will all be kept 
on the alert to listen, and the one reading will unavoid- 



110 HOW TO TEACH 

ably endeavor to pronounce correctly, enunciate dis- 
tinctly, and emphasize naturally. Additional effect 
will be given to the exercise by requiring the pupils to 
reproduce, in their own language, the substance of what 
is read to them. 

Where a simple system of diacritical marks is used 
in the Beading Book, the pupils should be taught to 
understand and apply them. An occasional brief re- 
view of the Eoman numbers, and of the names and 
signification of the marks used in punctuation, should 
be required. ^ 

The successful application of these suggestions in- 
volvBs the necessity of carefully grading the exercises 
and selections, so that the pupils be not required to 
read pieces which are above their comprehension. This 
is a point of the greatest importance. 



SPELLING. 

The exercises in spelling should be both oral and 
written, but principally written. 

The selections of words from the reading lessons 
should be so made that the class will not be prevented 
from advancing from one reading lesson to another 
with proper rapidity. When a Spelling Book is used, it 
should be made an auxiliary to the Reader, and not a 
substitute for it. If the lists of the Speller contain 
unusual words, these should be deferred until higher 
grades are reached. No time should be spent in spell- 
ing words which the pupil does not understand. 

For purposes of review, teachers should keep lists of 
those words of the lessons in which a large number of 
mistakes are made by the pupils. 



SPELLING. Ill 

In oral spellings care should be taken to name each 
letter distinctly, except in the -case of the "doubles/' 
which are to be distinctly pronounced as such, and not 
as " d'tlee '' for " douUe-e,'' " d'blow '' for " douUe-o;' etc. 

"Miscellaneous words'' should include the ordinary 
proper names of persons (not the surnames), words 
naturally suggested by those of the reading lessons, and 
common words of the daily life of the ht>usehold, the 
shop, and the street. The derivatives required should 
be those and those only which are in the commonest 
conversational use. They may be readily obtained by 
calling upon the class to suggest them. The modifica- 
tions of the primitives required in order to form them 
should be taught. 

The written exercises should be as neat as possible, 
care being taken to train pupils to habits of orderly 
arrangement of their work. When sentences are given, 
particular attention should be paid to the ordinary 
troublesome monosyllables, to the proper use of cap- 
itals, the sign of the possessive case, the period, the in- 
terrogation mark, and the use of the hyphen in a word 
divided at the end of a line. 



DEFINITIONS. 

In selecting words for definition, two leading pur- 
poses should be specially kept in view : 1. To impress 
or illustrate the particular meaning of the word as used 
in the lesson ; 2. To enlarge and correct the pupil's 
own vocabulary. 

Very simple words, such di^ father, water, Tcnife, Tcnee, 
looh, child, etc., the meaning of which every child already 
understands, should not, in the lower grades at least, 



112 £rOW TO TEACH 

be assigned for definition. Properly to define such 
words requires a nice discrimination in the use of lan- 
guage and a minuteness of analysis beyond the power 
of a young child. Teachers are apt to go astray in this 
direction. It is principally on this account that the 
limitation, " to teach the meaning of the words/^ has 
been introduced in prescribing this part of the grade. 
The written exercises will necessarily contain many 
such words, and thus the child will learn to spell them. 

Where a word has, in common use, two or more 
meanings quite diverse, a separate oral illustration 
should be required for each ; and where several words 
differently spelled have the same or a similar pronuncia- 
tion, a separate construction should be required for 
each in the written exercises. 

Defining one part of speech by giving another part 
of speech as a synonym, is a common error. It may be 
corrected or avoided by giving small groups of words, 
each consisting of a primitive and some of its most 
commonly used derivatives, and requiring, as an oral 
exercise, a phrase or a sentence to illustrate the use of 
each word in the group. 

Teachers should be particularly careful to comply 
with the direction, ^^ in no case to be committed to 
memory and mechanically recited.^^ The mere com- 
mitting of dictionary definitions to memory, or the sub- 
stitution for the word to be defined of another word, 
perhaps more difficult and unusual, is a perversion of 
the exercise. It is not only useless but pernicious, for 
it neither aids in mental development nor adds to the 
pupil's information, nor does it benefit him in his use 
of language. For this reason, the lists of words given 
in a spelling book for the purpose of teaching spelling 
are not well adapted for teaching the meanings of 



ABITHMETIC. 113 

words, these being most clearly corapreliended when 
the words are put into sentences or phrases. 

At this stage of the pupil's advancement, a full exer- 
cise on a given word should comprise the folloAving: 
1. Pronounce it; 2. Use it in the construction of a 
phrase or a sentence; 3. Detine it ; 4. Write a sentence 
containing it. [For the whole class.] 

In the performance of the written exercises required 
for definitions in this grade, the pupils may not only be 
taught the meaning of the words, but, by a skillful 
application on the part of the teacher, be prepared for 
the exercises in composition subsequently prescribed. 
This point should be kept in view. Correctness in the 
use of words, propriety in the thought, the accurate use 
of capitals, punctuation marks^ etc., should be invari- 
ably insisted upon. ■ 

ARITKMETIC. 

JHental Arithmetic. — The mental arithmetic 
should both precede and accompany the written arith- 
metic, step by step. The principal distinction between 
these two divisions of the subject is, that when the 
numbers involved are too great or too many to be readily 
retained in the memory, the slate should be employed 
as an assistant. 

"Exercises in rapid calculation without analysis'^ 
should, as far as possible, be of the most practical 
character. Examples given should be silently wrought 
by the whole class simultaneously as in written arith- 
metic, and the results obtained be written upon the 
slates, promptly, and at a given signal. The analysis 
can then be separately required of as many pupils as 
may seem expedient. 



114 no W TO TEA CII 

Ilhistration. — One method of conducting such an 
exercise is subjoined. Teachers fertile in expedients 
will devise others equally good, and involving the follow- 
ing important elements: 1. The exercise to be simul- 
taiTeous; 2. Silent; 3. Spirited throughout; 4. All 
copying, or wrongly claiming the answer prevented. 
The detail may be greatly varied : 

1. Pupils sit silent and erect; slates lying on desk, or. 
held^vertically, resting on the knees^ the hands being at 
the upper corners ; pencils in right hands. 

2. Teacher gives question with distinctness. 

3. Pupils work silently, remaining in position until 
the answer is found, when each silently raises the right 
hand, or stands. 

4. When sufficient time has been given, teacher says 

"Ready Write," with a pause between the words. 

At the last word the answer is instantly written in large 
figures, but only by those standing, or whose hands are 
up, and the slates instantly turned with the answer 
/toward the teacher. No further working or correction 
allowed. These movements are better executed, after a 
little practice, by using four light taps of the pencil, 
meaning, "Reacly," " Write," '' As you were," " Show." 

5. Teacher calls upon some one to read the answer, 
usually upon one whose results are frequently wrong. 
Those claiming the same stand if sitting, or raise the 
hand or the slate if already standing, the answer being 
still turned toward the teacher. 

G. If thought desirable, an oral analysis may now be 
demanded of any pupil, whether he obtained the answer 
or not. 

The explanatory or analytic statements made by the 
pupil should be of the simplest and most direct charac- 
ter consistent with clearness, and all unnecessary repe- 



ABITHMETia 115 

titions of formulae be carefully avoided. Where this is 
not done, the principal effort of the pupil is to recall in 
due order the set form of words, rather than to form the 
arithmetical combinations necessary to the solution. 

Besides simple examples in the four fundamental 
rules and Federal money, very simple operations in- 
volving practical applications of the selected tables of 
money, weight, and measure, should constitute a por- 
tion of the exercises in mental arithmetic. 

In the explanation or analysis of examples in mental 
as well as written arithmetic, the pupils should gener- 
ally be called upon, before solving, to state the question. 

Mental exercises in arithmetic should be conducted 
in a spirited manner. They should always have the 
character of extemporized exercises, and in no case 
form a part of the home-work of the pupil. 

Written Arithmetic. — The slates should be kept 
in the best condition as to cleanness; the figures should 
be distinctly and neatly made, and written in lines par- 
allel to the upper edge of the slate. A reasonable allow- 
ance should be made for imperfections in the forms of 
figures in those exercises where haste is required; yefc 
every eff'ort should be made to fix in the pupils habits, 
of care, neatness, and system in all that pertains to the 
written exercises. 

Exercises in adding columns of figures should be given 
with such frequency as may be found necessary to pro- 
duce and retain accuracy and rapidity. They should be 
in both forms — the silent and the oral. 

Every form of counting, whether by fingers, dots, 
marks, or other devices, should be strictly prohibited, 
and the class should be frequently tested for this special 
purpose. 



116 BOW TO TEACH 

The pupil should be allowed to name only the succes- 
sive results arising from the addition of the several 
successive figures, avoiding all that oral or mental repe- 
tition of the tables which is known as the "spelling 
process/' and all other unnecessary formulaa. 

Illustration. 
789 
457 
632 

178 

Correct Metliod.—^, 10, 17, 26 ; 9, 12, 17, 25, etc., etc. 

Incorrect Metliod, — 8 and 2 are 10, 10 and 7 are 17, 
17 and 9 are 26, set down the 6 and carry the 2, etc., etc. 
When this method is once fixed, it is difticult to change 
it. It acts as a clog to the mental activity of the pupil, 
who finds himself unable to think out the result in any 
other way. It is as if he should spell aloud every word 
as he reads. 

The above remark, i7a regard to the oral or mental re- 
petition of the tables, applies to all the fundamental 
rules and their applications. The processes should be 
reduced to the most concise form practicable. 

When pupils show an ability to add in two or more 
figures at a time, they should be encouraged to do so in 
exercises that are wrought out silently. 

When the divisor is less than 13, the long-division 
process is not to be employed or allowed. 

Short practical examples, involving two or more of 
the rules, should frequently be given, and in such a 
way as to cultivate the intelligence of the pupil. 

Examples requiring a very large number of figures 



ARITHMETIG. 117 

for their solution should be avoided, except as far as 
they may be necessary in order to give practical expert- 
ness. 

Examples should be given to test the pupils' accuracy 
in writing numbers requiring O's, and their knowledge 
of the proper methods where the multiplier or divisor 
contains O's. 

Exercises should be given to insure facility in read- 
ing and writing Federal money, and in reducing, by m- 
spedion and witliout analysis, dollars, or dollars and 
cents, to cents or to mills, etc., etc., and conversely. 
This reduction becomes important in certain cases in 
division of Federal money. (See Analysis B.) 

Analogous exercises in Federal money should be sub- 
stituted for those in the simple rules referred to in the 
preceding sections, as soon as may be found expedient. 

In all practical examples, instead of telling pupils to 
add, subtract, multiply, or divide, give the question in 
such a manner as to oblige them to exercise their own 
judgment as to the method and principle to be em- 
ployed. 

No detailed analysis is necessary in addition or sub- 
traction. 

Give short examples of bills of purchase or sale in- 
volving several items, and similar to those required in 
daily life. Let them be put into proper form on the 
slate, with names and date, and occasionally receipted, 
and the receipt explained. 

The following examples involve the points upon which pupils 
4are most apt to fail in the arithmetic of this grade. They are so 
highly important that a drill upon a series of similar examples 
is recommended. No pupil should be allowed to proceed fur- 
ther till he has thoroughly mastered them. 

Write 30,003,050— 700,500,00a 



118 BOW TO TEACH 

Multiply 30850 by 307 ; by 4070 ; by 2009. 

Divide 732427 by 200 ; by 40000, etc.— Should of course only 
be done by short division. 

Divide 732427 by 100; by 10000, etc.— Should only be done 
by pointing off. 

Write 3 dollars and 5 cents ; 10 dollars and 7 cents, etc. 

Bought for $2095.07, sold for $2500. How much did I gain or 
lose? 

Sold 320 bushels for $176. How much a bushel ? Analyze. 

Spent $42 for tea at 87i cents a lb. How many lbs. did I 
buy ? Analyze. 

Spent $8 for coffee at 40 cts. a lb. How many lbs. did I buy ? 
Analyze. 

If 24 yards cost $20.40, what will 17 yards cost ? Analyze. 

If 24 yards cost $20.40, how many yards can be bought for 
$14.45? Analyze. 

Note.— If fractions arise in the first stage of examples similar to the last 
two, they may be rejected in the second stage in this grade. 

The following are all the forms of arithmetical analysis neces- 
sary to the fifth grade : 



FORMS OF ARITBBIETICAL ANALYSIS 

FOR BOTH MENTAL AND WRITTEN ARITHMETIC. 

A. (Fundamental) — Multiplication. 

Question. — If one yard cost $3, what will 4 yards cost ? 
Analysis.— If one yard cost $3, 4 yards will cost 4 times $3, 
which are $12. 

Note.— Avoid the too concise form, '' will cost 4 times 3, which are 12." 
• B. (Derived) — Division. (1.) 

Question. — If one yard cost $3, how many yards may be bought 
for $12 ? 

Analysis. — If one yard cost $3, $12 will buy as many yards as 
$3 are contained times in S12, which are 4 yards. 

Note.— Avoid the too concise form *' as many as 3 are contained in 12/' 
Question.— Spent $42 for tea. at 87^0. a pound. How many 
pounds did I buy ? 



ARITHMETIC, 119 

Analysis. — $42 are 42000 mills, and 87i cents are 875 mills. I 
can buy as many pounds as 875 mills are contained, etc. 

See preceding " Suggestions " for remark about reducing Federal money 
without analysis. 

(7. (Derived) — Bimsioru (2.) 

Question. — If 4 yards cost $12, what will one yard cost ? 
Analysis. — If 4 yards cost $12, one yard will cost J of $12, 
which is $3. 

KoTE.— Avoid the very faulty forms "as much as 4 is contained in $12," 
or " times in $12," or *'4is contained in 12." 

Question. — If 5 lbs. cost $3, what will 1 lb. cost ? 
Analysis.— U 5 lbs. cost $3 or 300 cents, 1 lb. will cost i of 300 
cents, which is 60 cents. 

Combinations of A, B, and C. 

(J and A, Division and Multiplication. 

Question.— li 4 yards cost $12, what will 9 yards cost ? 
Analysis. — First by C for price of 1 yard, then by A for price 
of 9 yards. 

G and B. Division. (2) and (1). 

Question. — If 4 yards cost $12, how many yards may be bought 
for $27? 

Analysis. — First by C for price of 1 yard, then by B for num- 
ber of yards. 

Note 1.— Avoid set forms of giving questions. Vary the order of statement 
as far as is consistent with perfect clearness. For instance, the last question 
might have been put thus: Spent $27 for cloth. How many yards did I buy, 
if $12 bought 3 yards; or, How many yards for $27, if 4 yards cost $12? 
etc., etc. 

Note 2. — In this grade avoid examples in which fractions form a part of the 
quotient. 

Note 3.— It is frequently an assistance to some pupils to have them divide 
each question into conditions and demand— a.8 in C and A. " The condition is, 
that 4 yards cost $12. The demand is, what is the price of 9 yards." Such 
devices should be sparingly used. 

Note 4.— Analysis A and B apply to questions in the tables, substituting 
the word since for if. Examples : How many quarts in live pecks ? Since one 
peck contains eight quarts, five pecks contain, etc., etc. How* many feet in 
84 inches ? Since 12 inches make 1 foot, 84 inches contain as many feet, etc., 
etc. 



120 ^OW TO TEACH 



TABLES. 

In this grade, the tables of the preceding grade should be 
thoroughly reviewed, with the following additions : 

Time. — Teach about leap-year. 

Avoirdupois Weight, — 7000 grains = 1 pound ; 2240 
pounds = 1 old ton ; 62^ pounds, or 1000 ounces = 1 cubic foot 
of water. 

Troy Weight, — Explain its use, the great difference be- 
tween its pound and ounce, and those of Avoirdupois Weight, the 
grain beiug the only identical element. 24 grains = 1 penny- 
weight ; 20 pennyweights = 1 ounce ; 12 ounces, or 5760 
grains = Ipound. 

Apothecaries^ Weight, — Explain its use. Show that it 
differs from Troy Weight in nothing but the method of subdivid- 
ing the ounce. Teach that the fluid ounce is a measure, aud not 
a weight. 20 grains = 1 scruple ; 3 scruples = 1 dram ; 8 drams 
= 1 ounce ; 12 ounces = 1 pound. 

Long Measure, — Add the following : Explain the use of 
each term. 4 inches = 1 hand ; 3 feet = 1 pace ; 6 feet = 1 
fathom ; 1^ miles = 1 knot. 

Surveyors^ Long Measure, — 4 rods, or 66 feet, or 100 
links = 1 chain ; 80 chains = 1 mile. 

Surveyors^ Square Measure.— E^^l^m the local use of 
section and township. 16 square rods = 1 square chain; 10 
square chains =: 1 acre ; 640 acres = 1 square mile or section; 36 
square miles = 1 township. 

Solid or Cubic Measure. — Explain its use, and the 
difference in kind between the linear, superficial, and solid units of 
the same name. 1728 cubic inches = 1 cubic foot ; 9 cubic feet = 1 
cubic yard ; 128 cubic feet = 1 cord of wood ; 2150 cubic inches 
= 1 bushel ;. 231 cubic inches — 1 gallon. 

Angular Measure. — Teach the following terms : Circle^ 



GEOGRAPHY. 121 

circumference, quadrant, radius^ diameter. Teach the notation. 
Give examples in reading, as 16° 17' 45". 60" = 1 minute; 
60' = 1 degree; 90' = 1 quadrant; 360' - 1 circle; 360' = 
circumf. of the Earth ; 691- miles = 1 degree of latitude ; cir- 
cumference of a circle = 3f times the diameter. 

English Money ^ efc— The usual table. Teach the value 
of a pound sterling — $4.866|-. Teach the value of a franc — 18 
cents 6 mills. "^ 

If any foreign dollar is taught, let it be the thaler of Germany 
= 69 cents. 



GEOGRAPHY. 

General Suggestions for all Grades. — It 

is of the first importance that geography should be 
so taught and reviewed, as not to leave in the mind of 
the pupil a mere collection of facts, without mutual re- 
lation or dependence. On the contrary, he should, 
from the first, be led to consider the earth as man's 
dwelling-place — its motions as bringing him the neces- 
sary vicissitudes of day and night,- and the changes 
of the seasons — its land-sitrface as the chief theater of 
animal and vegetable life — the ocean as the world's broad 
highway, and the exhaustless source of clouds and rains, 
so necessary to every form of life on the land-surface — 
the great permanent air-currents as carrying to the 
land this moisture from the sea — the mountains as its 
condensers, as well as the chief source of mineral wealth 
— the springs and nt^^rs, with their branches, as carry- 
ing back again, and over the land, the ever-circulating 
water of the ocean — and of cities and toiuns, not as black 
dots on a map, in colored patches, which he has learned 
to call countries, perhaps near some crooked black 
streaks which he has learned to call rivers, but as the 

6 



122 B^OW TO TEACH 

centers of social life and development, the seats of 
government, and the crowded, busy hives of human in- 
dustry and intelligence. 

When geography is thus taught, it is one of the most 
interesting, important, and practical of studies; but if 
it is taught chiefly as. a description, by unvarying for- 
mulae, of long lists of rivers, capes, peninsulas, boundaries, 
etc., supplemented, perhaps, by a precise, verbatim repe- 
tition of the descriptive geography, as contained in 
even the very best text-book, it is one of the dullest and 
most unprofitable of studies. 

The text-book is a most important, and even indis- 
pensable auxiliary, but there is no more common and 
pernicious error, than that of siilstitutijig it in place of 
the teacher, who thus is degraded into a mere stupid, 
profitless, and mechanical hearer of lessons. The requi- 
sites for successful teaching are a globe, a blackboard, 
an outline map and pointer, and a good text-book. The 
pupil's first impressions should be formed from the 
globe, rather than from the flat and distorted repre- 
sentation of the map. When the text-book is to be used, 
and important and comprehensive lessons giveu, such 
as the presentation of the general outline of the world 
• as a whole, or of a continent or grand division, or of the 
United States as a whole, the subject should first be gone 
over orally, in outline, by the teacher. If this be done 
in a spirited manner* and the results carefully tested, the 
detailed study of the text-book will be greatly assisted 
and unified by the comprehensive view thus imparted, 
and the important details mpre surely remembered. 

Geography of tlie Fifth Grade. — In the 

preceding grade, the pupil has been taught the leading 
elementary ideas upon which geography is founded; in 



OEOGRAPHY, 123 

the present grade, these are to be reviewed, explained, 
and systematized, beginning with a general view of the 
world. The following is a syllabus of the points which 
should claim attention : 

Syllabus for the Fifth Grade, Part Ist.^The form of 
the earthy its magnitude^ the continents and grand divisions, their 
relative positions, their connecting isthmuses, and a few of their 
most important projections — the oceans, their positions, and prin- 
cipal arms and islands — five or six of the great mountain systems 
of America, and from eight to ten in the rest of the world ; three or 
four well-known volcanoes — about a dozen each of the chief n^^rs 
and straits^ and about half as many great lakes — from ten to a 
dozen of the most important cities of the world, and, in a very- 
general way, the location of the most important countries, such 
as the United States, Great Britain, Germany, Japan, China, etc. 
With each of these cities and countries some interesting or im- 
portant /ac^ should be at once associated. 

Part 2d, (To be taught as facts, in the simplest outline, and 
without attempting to explain according to any of the hypothe- 
ses of scientific physical geography, using the map and globe, 
whenever necessary, to impress any particular statement on the 
pupils' minds.) A brief notice of the ocean currents, their direc- 
tion, temperature, and use, pointing out only the equatorial cur- 
rent, one Arctic current, one Antarctic current, and the Gulf 
stream — the trade winds (very briefly), their location, direction, 
use in commerce, and their influence (in assisting to produce the 
great South American rivers, the Nile, etc.) — a general notion of 
climate, as affected by distance from the equator, and by eleva- 
tion — the motions of the earth, and the inclination of its axis — the 
zones, their limits, and a veiy few of their well-known and char- 
acteristic plants and animals, and, in a very general way, the 
location of the chief races of mankind. * 

^^ Outlines of North America.^^^First : Treat the con- 
tinent as a whole, pointing out its separate countries, most im- 
portant capes, peninsulas, islands, and arms of the sea ; its 
divisions into mountains, plateaux, and lowland plains, naming 
only a few of the most important of each. 



124 HOW TO TEACH 

Iceland, Greenland, Alaska, and all other Arctic Geography to 
be treated very briefly, and chiefly with reference to climate, re- 
sources, and people.— JVewfoundland; the Dominion of Canada, its 
surface, its provinces and territories, with their climate, resources, 
and people, and our trade with them ; the form of government ; the 
capital of the Dominion and those of the provinces, and the other 
most important towns; the commercial and international im- 
portance of the St. Lawrence River and the Great Lakes, and the 
small importance of the other rivers, of which three or four will 
be enough. 

United States.— A simple outline will embrace the follow- 
ing: 

Local Geography.— The boundaries of the country as a 
whole ; its dimensions in round numbers ; the location of the great 
mountain systems ; the western plateaux [a section of the country 
roughly drawn in chalk upon the blackboard will be found effi- 
cient] ; the high western plain; the low central plain; the eastern 
slope, and the California basin ; about a dozen of the chief rivers, 
with the great branches ; about five or six each of the great 
lakes, bays, and capes ; about twenty of the principal cities. 

Descriptive Geography will include a very brief descrip- 
tion of the highlands, lowlands, and drainage system already 
pointed out ; the climate and its gradual modifications by lati- 
tude, elevation, and distance from the sea ; and a general state- 
ment of the leading agricultural staples in the order of their 
latitude — rice, sugar, cotton, tobacco, corn, and wheat. 

Mexico. — Its surface, climate, resources, and people ; their 
language, government, and social condition ; about five or six of 
the principal cities. 

Central America very briefly; the names of its states and 
their capitals, and their general similarity to Mexico. 

West Indies^ the principal groups, about ten or a dozen of 
the most important islands ; five or six principal ports ; the 
climate, resources, and people ; their colonial relations, and their 
commerce with the United States, if important. 



LANGUAGE. 125 



LANGUAGE. 



Correction of Language. — In all the grades 
the pupils should be trained in the correction of Jan- 
giiage, and taught to avoid common errors of speech. 
This is best accomplished in connection with the dicta- 
tion ^aj^m^e.s required in the several grades ; also by oral 
exercises specially adapted to this purpose, and by inci- 
dental instruction during the recitations and lessons in 
other subjects, as in the definition exercises, the lessons 
in elementary science, etc. Indeed, every exercise in 
which the pupils are required to use their own language, 
either orally or in writing, shonld be made a vehicle for 
this instruction, the object being to impart the haiit of 
tising correct language. It is of the greatest importance 
that this habit shonld be acquired at an early age, for 
without it, the technical stndy of grammar will scarcely 
prove adequate to impart fluency in the correct nse of 
language. The old habits, in spite of the knowledge of 
principles and rules, will be always apt to show them- 
selves. 

On this account, teachers cannot be too careful them- 
selves in the nse of language. Their words as well as 
their acts should present a model for the imitation of 
their pupils ; and example in this, as in other things, 
will prove far more potent than precept. For special 
exercises in this department of the instruction, the fol- 
lowing suggestions are made : 

Write on the blackboard such faults in expression as 
are liable to be committed, including— 1. Ungrammati- 
cal expressions : as / liavenH no booh ; I licivenH got my 
'pencil ; I seen liim do it, etc. 2. Slang : This is an aivfui 
easy lesson, etc. The faulty expressions written in this 



126 HOW TO TEACH 

way should, however, consist of such as may have been 
committed by some of the pu^oils of the class, lest those 
who have acquired good habits of speech be contami- 
nated by having their attention called to such errors. 

Award premium marks, or some other kind of reward, 
to those who succeed in pointing out improper expres- 
sions on the part of their classmates ; but let this be 
done in the right spirit, and not for the purpose of 
subjecting any of the pupils to jeers or ridicule. The 
fact that their language may be made the subject of 
criticism by their fellow-pupils, will put all on the alert 
to use the best modes of expression in their power, and 
then correction will have a permanent effect in improv- 
ing them in the use of language. 

Sometimes one or more pupils may be selected by 
the class to act as censors for a definite period (say a 
week), and to call attention to errors made by any of 
the pupils of the class. The object of this and the pre- 
vious suggestion is to make the pupils critics on them- 
selves and others, most of the inaccuracies committed 
resulting rather from carelessness and inattention than 
from a want of knowledge. The teacher will, of course, 
often find it necessary to give direct instruction in rela- 
tion to certain expressions. 

Of coux'se, no instruction in technical grammar, or in 
any grammatical rules, is required until the next grade. 



ELEMENTARY SCIENCE. 

(By Oral Instruction.) 

Gekekal Suggestions eok all Grades. 

The leading object in this branch of instruction is to 
cultivate habits of olservation and reflectio7i, and to give 



ELEMENTARY SCIENCE. 127 

facility in oral description. Avoid everything tend- 
ing to convert these lessons into recitations of set forms 
of words, however these forms may have been obtained, 
however well they may be understood by the pupils, and 
however important the facts thus stated. 

'^Familiar oijects,^^ and familiar animals, plants, and 
minerals take precedence of all others in the selection 
of topics. 

It is neither possible nor desirable to attempt to teach 
all, or even the greater part of the topics that might be 
classified with the requirements of any grade. No topic 
should be treated exhaustively, nor should the topics 
selected be so few, or so frequently reviewed, as to nar- 
row down or suspend the discipline of the observing 
faculty. The selection and limitation must be left to 
the good sense of the teacher. 

The objective method of teaching presents two dis- 
tinct, though intimately related departments. Percep- 
tive teaching, in which the object, as an acorn or an ^gg^ 
is directly presented to the pupils' senses ; and conceptive 
teacliing^ in which impressions previously received are 
recalled, arranged, and utilized, the objects themselves 
not being presented to the senses during the lesson. 
An oak, an elephant, or a thunder-storm, would fall 
under the latter department. 

The use of pictures^ models^ or other sensible repre- 
sentations of objects, constitutes an important combina- 
tion and modification of the two principal methods, 
and should be often employed. 

Definitions should be very sparingly introduced, and 
never in the first stage of a subject. If given at all, 
they should sum up knowledge already attained. Tlie 
terms organic, inorganic, vegetable, animal, and mineral, 
are prominent among the very few terms requiring defi- 



128 SOW TO TEACH 

nition. Such definitions should be prepared for by a 
process at once inductive and objective. 

No fact which the teacher can readily lead the pupil 
to discover for himself, should be imparted by the 
teacher. Importmii facts not readily derived from the 
pupil's own observation, must, of course, be supplied by 
the teacher. Avoid overloading a topic by details. No 
topic should be selected in which the number of facts 
to be told bears a large proportion to those which the 
pupil may be led to discover for himself. 

The language used hy the pupil should he entirely his 
oton, excepting, of course, the few indispensable defini- 
tions. 

The process einployed will present two distinct stages : 
First, the analytical or preparatory, in which the teacher 
leads the pupil by questions to discover or to remember 
the properties or peculiarities of an object, or to state 
any other important facts associated with it. The re- 
sponses by the pupil will be, of course, in his own words ; 
and the additional statements which the teacher him- 
self may find necessary to make, will be given in the 
form of conversations. This stage gives the principal 
discipline of the powers of observation and reflection. 

The points thulS considered, and the facts thus stated 
should be written upon the blackboard in the briefest 
possible synoptical form, but each only after it has been 
considered. While some such synopsis is indispensable 
to the teacher as the first step ol preparation for giving 
the lesson, it should never be presented to the pupil ex- 
cept by the gradual process above indicated. 

The second or revieiu stage of the process is based upon 
the results of the first, and furnishes the principal dis- 
cipline of the powers of description or oral statement. 
The facts already considered should be re-arranged, if 



ELEMENTAR Y SCIENCE, 129 

necessary, into an orderly synopsis upon the black- 
board, the pupils being called upon to assist in this 
arrangement. They should then be required, in turn, 
to state what they can recall of each item of the synop- 
sis, then of each group of items, and, lastly, of the whole 
subject. Then the synopsis may be wholly or in part 
removed or hidden, and the oral process of review re- 
peated. As a final stage, and before dismissing the sub- 
ject, an extempore coinpositioii, with or without the aid 
of the synopsis upon the board, should be written by 
each pupil upon his slate. 

Outlines of Zoology, 

In relation to this part of the fifth grade, the fol- 
lowing suggestions are made : 

Zoology being a science of classification, it is indis- 
pensably requisite to teach the distinctions upon which 
the classification depends. 

Only the simplest outline need be taught, with such 
facts and details as seem most naturally appropriate to 
illustrate the subject. 

The process of classification being naturally oljective, 
that is, animals being classified by their obvious pecu- 
liarities, the pupil should be led, by an exercise of the 
observing faculties, to discover the leading peculiarities 
himself. 

For instance, suppose the teacher wishes to lead to 
the perception of the basis of the classification into 
the four great types or sub-kingdoms. Write upon the 
blackboard the names of a sufficient number of fa- 
miliarly known animals without classification. If he 
have their pictures in books, or on charts, let each be 
shown before asking and writing its name. Let the 

6* 



130 HOW TO TEACH 

pupils spell each name before the teacher writes it. Sup- 
pose them to be lobster, ox, oyster, dog, beetle, starfish, 
snail, and corah Lead the pupils to see and decide for 
themselves which two or three most resemble each 
other. Adroit questioning, and a little patience, will 
soon make them group together the lobster and the beetle 
on account of their hard, jointed rings, and their many 
equally hard limbs ; the ox and the dog, from their 
four legs, and their similarity as to eyes, ears, and other 
organs ; and the oyster and the snail, from their hard 
shells and soft bodies. The remaining starfish and coral 
will present difficulties, because not so familiarly known ; 
but these may readily be overcome by the use of pic- 
tures or even rough sketches on the board. 

Having thus grouped the names upon the blackboard, 
a few questions will lead to the perception that the ani- 
mals of one group have a backbone, composed of many 
pieces, and an internal bony skeleton ; those of another 
are made up of distinct rings and joints ; and so on of the 
other groups, each of which may now be readily ex- 
panded, by asking the pupils for the names of other ani- 
mals, and the reasons for assigning them to a particular 
group. 

Then, akd kot till THE:sr, the teacher should give 
and explain the terms vertebrate, articulate, etc., care- 
fully reviewing and questioning the class, to see that all 
is understood. 

In the same manner, the classes of the vertebrates, and 
the principal orders of the mammalia, etc., may easily be 
drawn from the pupil's own observations of resem- 
blances and differences. 

The terms 7mneral, vegetable, animal, organic, and in- 
organic, should be previously taught or reviewed in a 
similar manner, through the perceptions of the pupil, 
guided by the questions of the teacher. 



ELEMENTARY SCIENCE. 131 

• 
Rememler that the shillful use of interrogation is 

the teacher^s chief means of aiuakening thought, and pro- 

ducing lasting impressions. 

Well-known typical animals should be taken as the 
objective basis of the classification ; such as man, 
monhey, hat, cat, rat, horse, deer, coiv, and luhale ; — 
eagle, parrot, canary, rooster, ostrich, snipe, and duck ; — 
turtle, alligator, rattlesnake, and frog; — perch, cod, shark, 
etc. ; — iee, butterfly, beetle, etc. ; — spider, cray-fish, and 
crai; — squid, snail, and oyster ; — starfish, jellyfish, and 
corals. 

The simplest names should be used, where possible, in 
preference to the more scientific, or, at least, as pre- 
paratory thereto ; thus, it is better to use the term four- 
handed than quadruynana ; ^ gnaivers than rodentia; 
scratchers than rasores ; two-winged than diptera, etc. 
A few scientific terms, such as mollusc and bivalve, are 
in such common use that they may be readily explained 
and applied. 

Associated facts not strictly scientiiic — such as the 
uses of animals, anecdotes concerning them, their pecu- 
liarities and habits — which the pupils themselves may 
have observed, will form a valuable part of these exercises, 
and a means of increasing the interest of the lessons. 

The pupils should be encouraged to acquire as many 
facts as possible by their own observation and research 
out of school. 

The exercises should be conversatmial, the reviews 
frequent ; the instruction should also embrace exercises 
in classifying well-known animals from a miscellaneous 
list, giving the reasons in each case. Too much ground 
should not be attempted at first. 

Some system of diagrams, roughly sketched in chalk, 
will be found of great service in assisting the pupils to 



132 HOW TO TEACH 

remember the classification. The best and simplest is, 
probably, that used in the ordinary " genealogical tree/^ 
The diagram should be gradually developed as the 
lessons proceed, and not the whole of it -given in the 
preliminary stages. 

No teacher can give such a classified " outline" with- 
out having first, by careful study, acquired it. This 
can be readily accomplished by means of any good school 
manual on the rudiments of Natural History. 

Excepting in important instances, it is not expected 
that the classification should extend to species and 
variety, sometimes not even to genera. It is desirable 
that the pupils should have some definite ideas as to the 
relations of the following terms used in zoology : hing- 
dom, branch or type, class, order , family , genus, species, 
variety, ' individual. These can be best exhibited by a 
diagram, but they should in no case be presented by 
formal definition. All but the last four should ^^e 
mentioned in describing any given animal. 

The exercises should include a portion, at least, of 
the topics suggested in the following synopsis, which is 
here presented for the guidance of the teacher. This 
synopsis comprehends three successive outlines, each 
complete in Itself, or taken with that preceding it : 



First General Outline. 

Distinction of organic and inorganic objects taught objectively. 
Differences between animals and plants. What is an organ ? An 
animal? Four great types of animals (Cuvier's, and omitting the 
protozoa). Exercises in classifying, by types only, such animals as 
the dog, lobster, clam, coral, shad, wasp, goose, starfish, garter-snake^ 
slirimp, toad, tortoise, oyster, etc. The reasons for the classification 
should be given in each case. Each type to be then briefly de- 
fined. Why vertebrates are placed first. 



ELEMENTARY SCIENCE, 133 



Second General Outline. 



Classes of Vertebrates* — (Tenney's arrangement is here 
selected as being brief and simple, but any other may be taken.) 
Illustrate, as by types, by mentioning animals belonging to the 
several classes, mammals (those which feed their young with 
milk), birds, reptiles, batrachians (frog kind), fishes ; brief de- 
scription of each class to be given. Name common vertebrates 
to be classified, occasionally mentioning an animal not a verte- 
brate, in order to test the attention and accuracy of the pupils ; 
for example : alligator y roUn, mouse^ worm, herring^ toad, lion, 
jelly-fishy rattlesnake, elephant, fi£a, hawk, turtle, etc., etc. 

Classes of Articulates to be treated very briefly, but in 
the same manner as the vertebrates. Simplest division, as in- 
sects, Crustacea, and worms^ to be employed. 

Classes of Molluscs.^Tvesit also briefly, by referring only 
to their general characteristics. Teach the meaning of the tei-ms 
univalve and bivalve. Specimens of shells will be useful for illus- 
tration ; but it must be remembered that the structure of the ani- 
mal itself is far more interesting and important than that of the 
shell which incloses it. A living oyster or clam, opened and 
carefully examined, a living snail, and a tumbler of water con- 
taining a few of the small molluscs found in every pond, will 
give clear ideas. A small aquarium will be found very useful. 

Classes of MadiateSf probably treated with suflBlcient full- 
ness in connection with types. Review if necessary. 

Here it would be well to mention the grouping of animals as 
herbivorous,, carnivorous, and omnivorous ; also the general rela- 
tions of the ieeth of animals to other peculiarities, such as feet, 
forms, food, digestive apparatus^ and habits ; also, as far as may 
be possible, illustrations of the importance of their several func- 
tions in nature. 

« 
Third General Outline. 

In this outline some orders should be omitted, or but briefly 
considered, because not readily treated objectively. If all the 
prescribed classes cannot readil}'' be taught, owing to the limited 



134 HOW TO TEACH 

available time, selections sufficiently complete in themselves 
may easily be made, as of the class mammals, or bii'ds, or of the 
type articulates. 



Mammals. 

Two-handed (Bimana).'-'To be treated briefly. The five races 
of men, with their characteristic peculiarities. The geographi- 
cal distribution of each to be also briefly referred to. 

Four-handed (Quadrumana.)—A few examples, according to 
the experience of the pupils. Refer to the geographical distri- 
bution. 

Hand-winged {Cheiroptera),— TJse a drawing, or a dried, or a 
living specimen, if one can be procured. Any interesting facts 
about bats, and their nocturnal habits. 

Insect-eaters (Insectivor a). ~Trea.t very briefly. The mole^ its 
habits — refer to its small, hidden eyes, etc. 

Flesh-eaters {Garniwra).—To be treated more fully. Refer to 
general structure of teeth, feet, and stomach. Refer to cat family, 
using common cat as type ; dog family^ using dog as type ; weasel 
family, their form, habits, etc., naming sable, marten^ ermine, and 
minky and referring to the value of their furs ; bear family ; also 
briefly to seal family. 

Pouched Animals (Marsupials). — Refer to the geographical dis- 
tribution. The exception of the opossum. 

- Gnawers (Rodents).— Vse the rat or squirrel as a type. Refer 
to peculiarity of teeth, and the provision for their continued 
growth. Teach about the rat, mouse, squirrel, beaver^ rabbit. Re- 
fer to the woodchuck, porcupine, and guinea-pig. 

Thick-skinned (Pachyderms).— -Tve^i briefly of the elephant, the 
rhinoceros, and swine families ; more fully of the horse family, in- 
cluding Aors^, ass, and zebra. Geographical origin of the horse, 
its dispersion, and its influence in human affkirs. 

Gud-chewers (Ruminants). — Relations of food to teeth, stomach, 
feet, etc., etc. Teach three families : 1. Deer family, horns solid, 
deciduous ; 2. Hollow-horned family (horns permanent) ; 3. Camel 
family (hornless). Refer to llama and vicuna. 

Whale-like (Cetacea). — Refer to the fish-like character of the 



ELEMENTARY SCIENCE. 135 

whale ; how it differs from a fish ; its uses. The porpoise and the 
dolphin. 

Note.— Two of the preceding orders (8th and 9th), are sometimes classified 
under the following arrangement, which may be readily substituted for the 
above if thought desirable. 

Hoofed (Ungulates) into two sub-orders : A, cud-chewers (Ruminants), and 
B^ (Non-Ruminants). These are again divided into the following groups of 
families:— 

A. (Hollow-horned) ox, sheep, and antelope families. 
(Solid-horned) deer, girafi'e families. 
(Hornless) camel family. 

B. (Solid-hoofed) horse family. 

(Thick-skinned or Pachyderms) elephant, swine, hippopotamus, rhinoceros, 
and tapir families." 

Birds. 

Birds of Prey (Raptores). — ^Vulture, falcon, owl, condor, hawk, 
eagle. 

Climbers (Scansores). — Parrot, woodpecker, etc. 

PercTiers (Insessores). — Humming bird, swallow, kingbird, 
thrush, sparrow, canary, etc. 

Scratchers (Rasores). — Gallinaceous birds and dove family. 

Runners {Cursores).—0^iv\Q\\ ; its habits. 

Waders {Grallatores). — Crane, stork, snipe, etc. 

Swimmers (Natatores). — Duck family : Swan, petrel, penguin, 
albatross, etc. Refer to nests of birds, also their migrations, in- 
siincty etc. 

Reptiles and Frog Family. 

Treat very briefly, teaching something of turtles, crocodiles, 
and alligators ; serpents and their fangs ; the frog and its trans- 
formations. 

Fishes. 

Treat the classification very briefly ; show distinction between 
the two groups, bony and cartilaginous fishes, with the orders 
spine-finned and soft-finned ; also the shark and the sturgeon. 

Articulates. 

These present many advantages for the school-room. They are 
small, and easily procured for perceptive teaching. A simple 



136 BOW TO TEACH 

microscope is of great assistance in awakening an interest. Of 
insects, collections of type specimens can easily be made. Only 
the simplest and most interesting facts) however, need be taught. 
The general characteristics of this class of animals should be ex- 
plained—their structure and the functions of their chief organs. 
Their wonderful transformations should be explained and exem- 
plified; also the difference between insects proper^ spiders^ and 
many-footed articulates {myriapods). 

The following orders should be taught and exemplified : 

1. Memhrane-winged {Hy menopter a). —Inclw&mg the bee family, 
the ant family, the wasp family, the ichneumon family, their 
peculiarities, habits, and instinct. ^ 

2. Scale-winged {Lepidoptera). — Moths and butterflies, how dis- 
tinguished ; caterpillars, etc., clothes-moth, geometer. 

3. Tiw-winged {Biptera).— Mosquito family, . wheat-fly, house- 
fly, etc. 

4. Case-winged {Coleoptera). — Beetle, fire-fly, weevil, etc. 

5. Half-winged {Hemiptera) ; or bugs, cicadas or harvest-flies, 
tree-hopper, cochineal, boat-fly, etc. 

6. Straight-winged {Orthoptera). — Cricket, katydid, locust, grass- 
hopper. 

7. Net-winged {Neuroptera). — Dragon-fly, May-fly. Kefer to the 
white ants. 

Spiders {Arachnida). 

Many-footed Insects {Myriapods). — Centipedes. 

Crustacea. — Crab, lobster. 

Worms. — Earth-worm. 

Note. — It is important to distinguish carefully the three terms, insect (i. e., 
six-footed [hexapod], or true insects), arachnids, or eight-footed spiders and 
scorpions, and myriapods, or many-footed millipeds and centipedes. In using 
a representative of one of these groups as an object, it should be the primary 
aim to establish the obvious characteristics by which they are distinguished 
firmly in the pupils' minds. Thus, in the insect proper, the body is divided 
into three divisions — the head, the body (or thorax), and the hind-body (or 
abdomen). The head is furnished with feelers, {antennce) ; the body supports 
three pairs of legs, and generally one or two pairs of wings ; the abdomen 
shows more or less clearly a number (seven) of rings or joints. In the arach- 
nids, the head and body are consolidated into one division, which has no 
antennae, supports four pairs of legs, but no wings. In the myriapods, the 
entire body consists of a series of very similar joints, not grouped into divi- 
sions separated (insected) from one another, but of which the first serves as a 
head, whilst each of the others, lu)wever numerous, supports either one or 
two pairs of more or less imperfect legs. 



FOUETH GEADE 

OUTLINE COUKSE. 
Time allowed^ about five months. 



LANGUAGE. 

Heading. — Of the grade of a Third Reader (latter half), with 
exercises as in the preceding grade. 

Spelling and Definitions.— Yvom the reading lessons, 
with exercises in miscellaneous words and sentences, as in the 
preceding grade. Also easy exercises on the prefixes and 
suffixes, and then* applications. 

"English Grammar. — To include the analysis, parsing, and 
construction of simple sentences, and with such definitions only 
as pertain to the parts of the subject studied. 

ARITHMETIC. 

Mental Arithnietie. — As far as in written arithmetic, with 
exercises as in the Fifth Grade, including practice in the simple 
applications of the tables of weight, measure, money, etc. 

Written Arithmetic. — Common and Decimal Fractions, 
with their simple practical applications, and their conyersion one 
into the other. Also, practice in the simple rules and Federal 
Money, for the purpose of securing rapidity and accuracy. 

GEOGRAPHY. 

Geography. — Of the United States in detail. Local and 
descriptive geography treated as in the Fifth Grade. 



138 ^OW TO TEACH 



ELEMENTARY SCIENCE for oral instruction. 

botany. — An outline knowledge of Botany, including the 
general structure and common uses of such plants as most 
pupils may readily observe. 

This should, if possible, be taught during the spring and 
summer months, in order to make it in the highest degree ob- 
jective by the use of specimens. 

Mineralogy. — A simple outline knowledge of Mineralogy, 
illustrated by specimens. 

This may constitute the fall and winter course, the specimens 
being previously collected. When the time permits the teaching 
of only one of these branches, the season of the year should 
determine the choice between them. 



WRITING. 

On Slates. — Continued with practice, to give expertness and 
fluency. 

On I^aper. — Eeview of the elementary forms ; their com- 
bination in words containing long and short letters, without 
capitals ; next, in words containing both capitals and small 
letters ; an explanation of the elements involved in each. 

Instruction as to proper position, holding the pen, etc., as in 
the preceding grade. 



DRAWING. 

On Slate or JPaper. — Review of the Fifth Grade as far as 
may be necessary, and drawing curve lines, and figures formed 
from them, as the circle, ellipse, etc. 



SPELLING. 139 



How TO Teach. 



SUBJECTS OF THE FOURTH GRADE. 



LANGUAGE. 

Reading. — See directions and suggestions given 
for the Fifth Grade. 

The latter half of a Third Eeader usually comprises 
selections appropriate to this grade. Particular atten- 
tion should be given to clearness of articulation, to 
naturalness of intonation, and to general style. 

Spelling. — The exercises in spelling, both oral and 
written, should be the same as in the previous grade, 
with the following additional suggestions. The names 
of important cities, states, and countries, which occur 
in the geographical lessons of the class, and especially 
such as are in frequent use in post-oflBce addresses, or 
are liable to be mis-spelled, should form a part of the 
miscellmieous loords taught in this grade ; also, familiar 
personal names. An excellent occasional modification 
of this exercise is, to have the pupils draw the out- 
line of a letter-envelope upon the slate, or use a neatly- 
trimmed piece of writing paper of the same shape, and 
direct it to some person whose address is given by the 
teacher. The ingenuity of the teacher will suggest 
many other similar modifications of the exercise. 



140 HOW TO TEACH 

Definitions, — These should be as in the previous 
grade, with the following additional exercises designed 
to lead to the study of etymology. 

'' The easy exercises on the prefixes and suffixes ^' 
should be with English primitives at first, without re- 
gard to the etymology of those primitives. The affixes 
of Anglo-Saxon origin will therefore be taught first ; 
afterward the meaning of such as ab, co7i, pre^ pro, sub, 
ion, ent, etc., may be taught as illustrative of the diver- 
sity of meaning of such words as abstract, subtract, con- 
cede, accede, precede, etc. Also as showing that, for 
example, all words having the prefix sub convey the 
signification of under, and all having the suffix ion 
mean the act of. 

2. Each group, with its common radical or primitive, 
after being written on the slate or blackboard, should be 
made the subject of an oral exercise in definitions, in 
order to impress upon the pupils' minds the modifica- 
tions of meaning produced by the affixes. The exem- 
plification of the words in sentences should be also care- 
fully attended to. 



JEnglish Grammar. — The instruction in this 
subject required for the Fourth Grade includes cmalysis, 
parsing, and constructioji, and in the order mentioned. 
Grammar is the science of the sentence ; and, therefore, 
the fundamental idea to be imparted is, ivhat consti- 
tutes a sentence. Oral lessons should precede the study 
of the text-book, as a preparation for it. The ideas in- 
volved in the definitions should first be developed, before 
the pupils are required to commit these definitions to 
memory. The contrary practice, once so common, is 



LANGUAGE, 141 

very discouraging and injurious to the pupil, since it 
compels him to learn by rote a mass of verbiage which 
is perfectly unintelligible to him. 

Let a short sentence be written on the slate or black- 
board ; and then, by analysis, let the pupils be made 
familiar with the relations of the words used as subject^ 
verb or predicate, and adjuncts, or modifiers. The dis- 
tinctions comprehended in the parts of speech can all 
be successively taught in this way, and the pupil en- 
abled readily to point them out, before he is required to 
say what a noun, or pronoun, or verb, etc., is. The 
learning of the definitions will be easily accomplished as 
he proceeds. 

The object of the analysis is to find out in what rela- 
tion the words used in the sentence stand to one another 
(general grammar); the object of the j^^arsm^ (only an- 
other kind of analysis) is to apply the principles and 
rules proper to these relations (particular grammar) ; the 
object of the construction is to impart practical skill in 
applying these rules and principles, as well as to give 
thereby clearer ideas of their nature and use. Thus, 
when the teacher presents the sentence, " Industrious 
pupils learn very rapidly,^^ the pupil is made te discover, 
first, the principal parts — subject and verb, or simple 
predicate ; next, that industrious is added to pupils, 
rapidly to learn, and very to rapidly. The pupil then 
knows that vadustrious, being an adjunct of a noun, is 
an adjective ; that rapidly, being an adjunct of a verb, is 
an adverb ; and that very, being an adjunct of an adverb, 
is also an adverb. This instruction can be supplemented 
by requiring the pupils to construct sentences of a 
similar kind ; as, sentences containing a simple subject 
and predicate, — sentences containing a subject and ad- 
juncts with a simple predicate, — sentences containing a 



143 HOW TO TEACH 

subject and predicate, with adjuncts of both. Some of 
these sentences may be required to be declarative, some 
interrogative, etc. In this way the ingenuity or inven- 
tion of the pupil is brought into play in connection with 
his knowledge of grammar ; and the exercises glide pro- 
gressively into extended composition. 

The sentences presented should at first be carefully 
classified, so that no difficulties maybe presented which 
are beyond the pupils' ability or actual attainments to 
solve. In grammar, especially, should the instruction 
be systematic and logical. 

Etymological exercises should be interspersed, espe- 
cially in the use of the apostroplie as the sign of the 
possessive case — in the proper plural termination of 
nouns — the proper forms of the pronouns, etc. This is 
a point of considerable importance. 

The sentences required to be studied in this grade in- 
clude : 

1. Sentences with a simple subject and a simple pred- 
icate; 2. Those with simple word adjuncts of either sub- 
ject or predicate, or both ; 3. Those with simple phrase 
adjuncts (so as to teach the preposition) ; 4. Those 
with compound subjects or compound predicates, or 
both, but of an easy character ; as, "John, William, and 
Samuel are diligent boys," — "The animals turned, look- 
ed, and ran away.'' This class of sentences will serve 
to introduce the conjunction. 

It is especially requisite in all the lessons given on 
this subject, that the instruction should not be allowed 
to degenerate into the repetition of formulae, and instead 
of being made a means of developing the analytic and 
reasoning faculties of the pupils, become a piece of 
worse than useless mechanism. Grammatical instruc- 



LANGUAGE. 143 

tion has a distinct office as an educational agent, — an 
office that can be performed by no other subject. It is 
addressed to faculties that probably cannot be trained 
in any other way ; and, therefore, no educational cur- 
riculum would be complete without it. It should, how- 
ever, be carefully kept within proper limits, both as to 
time and place, and should not be permitted to encroach 
upon other branches of equal importance. Each depart- 
ment of it should also have its due share of attention. 

Of course the study of grammar as prescribed in this 
grade does not supersede the " exercises for correction '' 
required in all the grades. These exercises, however, 
by degrees lose their empirical character, and become 
scientific. They should not be exclusively either ety- 
mological or syntactical, according to the technical dis- 
crimination followed in most text-books on English 
Grammar. Indeed, nothing has done more to bring 
upon this study an unmerited depreciation, as being a 
senseless waste of time, than the unwise separation of 
these correlated departments of the subject. 

For instance, instead of teaching the declension of 
the pronouns 7, thou, he, and she, long before the appli- 
cation of any syntactical rule, the diversities of inflec- 
tion and their proper use may be observed and studied 
by the pupil in connection with the ordinary analysis 
of simple sentences, and consequently at a quite ele- 
mentary stage of the study. The transformation of 
*^ John can see James '^ into "/can see him,^^ will teach 
him the nature of a pronoun, how to distinguish it, and 
then how to define it. An attempted change of places, 
as in "Him can see V when taken in connection with 
the analysis, will show him the reason of the change of 
form from he to him and from / to me. 

Similar exercises upon the other pronouns, used in 



144 HOW TO TEACH 

both numbers, will lead him to see that each of them 
takes one form when used as the siilject of a sentence, 
and a different one when used as the oljed. He will 
then be ready to use intelligently the terms singular, 
])lural, nominative, and ohjedive, as applied to varied 
inflections, and to correct such errors as, " Who saw 
him ? Me.^^ " Me and her saw him,'' etc., as well as to 
give the reason for such corrections. Then, and not 
till then, can he be profitably required to construct, re- 
peat, and explai7i the declensions of the pronouns. A 
similar plan should be followed in the comparison of 
adjectives and the conjugation of verbs. 

A few common errors are subjoined as a further illus- 
tration of the kind of work proper to this grade. 

Errors in Etymology. — 1. The Possessive Sign. A goos'es 
foot. Three geeses' heads. Two fox's tails. A mans hat. 

2. Improper form of tenses. They done it. We seen him. 
He would have went. If I had have seen it. 

3. Improper use of verbs. He must set still. The book lays 
on the desk. He laid still. 

Errors in Syntax. — 1. Subject. Me and her can sew 
2. Predicate. We was there. He don't know. She dare not 
do it, 3. Ol^ect. He struck my brother and I. Who did you 
see 2 Attribute, If I were him. She looks beautifully. 



ARITHMETIC. 

JKental Arithmetic. — The character of the ex- 
amples to be given in this grade is suggested by the 
exercises in Written Arithmetic. The same processes 
and forms of analysis should be employed in both. In 
connection with the commonly-used tables of weight, 
measure, etc., should be given such questions as, " In 
f of a pound of sugar, how many ounces?^' ^^18 
quarts are what part of a bushel ? ^^ etc., etc. 



ARITHMETIC. 145 

Written A-Vithinetic. — Federal Money should 
also form a part of the regular work of this grade at 
least once a week, and should be frequently reviewed. 

Particular care should be taken in the selection of 
examples that no one of them be so intricate and prolix 
as to consume a large amount of time, without afford- 
ing sufficient exercise of thought in the application of 
arithmetical principles. 

Too much importance, nevertheless, can scarcely be 
given to the requirement of '^practice for rajoidity and 
accuracy ^^ in Federal money, as well as the simple rules 
of Arithmetic. To this should invariably be assigned a 
brief portion, at least, of the time given to every lesson 
in this subject. No part of the arithmetical discipline 
has a higher utilitarian value, whether for the purposes 
of practical life, or for progress in the more advanced 
portions of the study ; for nothing is more discouraging 
to the pupil than to find that, in any exercise involving 
other than a few figures, his results are almost always 
incorrect, from a want of habitual accuracy in perform- 
ing the simple combinations involved in the elementary 
rules. Teachers are, therefore, especially advised to 
employ every variety of proper stimulus to make the 
exercises for this purpose thorough and effective. 

For general suggestions see the preceding grade. 

Common Fractions. — N"o part of the study of 
arithmetic is of more importance than the subject of 
fractions. When properly taught, their value, as a 
mental discipline, is of the highest order. When 
taught merely, or chiefly, by memorized formulae, 
called " rules," they are, for the greater part, a waste 
of precious time. 

No ;principle should le ijresented until the pupil is 



146 HOW TO TEACH 

about to make use of it, and no definition sliould he given 
or required before tlie ideas which it embodies have been 
deduced, and clearly presented by preliminary illustra- 
tion and questioning, 

No rules should be giyen until a sufficient number 
of examples for practice have made them a succinct 
statement of 'principles previously understood, or the 
results of the application of principles, rather than mere 
mechanical formute for working. 

In teaching the fundamental principles of fractions 
the objective process is indispensable. 

The most effective method of treating the subject as 
a whole, is to give first a very simple outline coiirse of 
exercises, covering all the essential principles, but by 
means of examples requiring only small numbers for 
their solution. Such examples, though readily solved 
mentally, after some practice, should, in tlie first stages, 
be wrought upon the slates, in order to secure correct- 
ness in notation, and to allow the pupil more easily to 
give the necessary analysis without the additional men- 
tal tax required by the effort to retain the numbers. 

In the written exercises pupils should use the signs 
of operation, + — x -f-, and the sign of equality, to 
indicate the work performed, and its result. 

This outline should then be followed by ^full course, 
in which the substance of the first constitutes the exer- 
cises in mental arithmetic, while the written arithmetic 
compi'ises the more difficult portions of the general sub- 
ject, as well as a systematic statement of definitions 
and rules, and practical examples, involving numbers 
too large to be readily retained in the memory. Such a 
plan, though apparently long, is in reality the most ex- 
peditious. The pupil soon obtains a clear, comprehen- 
sive, and connected view of the essential principles, and 



ARITHMETIC, 147 

the expanded review which constitutes the second 
course will then require but little time. 



Syllabus of Topics for Outlines of Commoi^t 

Fractio:n's. 

(with suggestions and examples.) 

I. — The idea of a fractiou developed objectively. 

The equality of the parts to be very carefully illustrated. 

The relative value of various fractional parts, as greater or less, 
^s "3, 5-, yo) etc. 

The definition of a fraction. One or more of the equal parts 
of a unit. 

The terms of a fraction defined- 2in6. the order of statement. 

The notation of fractions and location of terms, or order of 
writing. 

Exercises in wi'iting and explaining fractions. 

Fractional expressions less than a unit. 

Proper fractions defined, and examples. A proper fraction is 
one that is less than a unit 

Fractional expressions equal to or greater than a. unit. 

Improper fractions defined and illustrated. An improper frac- 
tion is one that is equal to, or greater than a unit. 

Exercises in writing proper and improper fractions. 



n 
II. — Fundamental Axiom 1= - 

n 

Reduction of units to improper fractions. — Analysis A. 
(Page 152.) 

Reduction of mixed numbers to improper fractions.— ^r^-a^i/m A. 
Definition of mixed numbers. 

Exercises in mixed numbers, limited to small denominators. 
Reduction of improper fractions to mixed numbers. — Analysis B. 
(Page 152.) 



148 HOW TO TEACH 

III.— Reduction effractions to greater denominators — or higher 
terms. [What may halves, thirds, etc., be changed into ? I^'s ? etc.] 
To be illustrated objectively. 

Examples with greater denominators than can readily be solved 
by inspection. 

Analysis C. (Page 152). (Begin with fundamental axiom.) 

Term Dimsor or Factor , with exercises in finding, by inspection 
only^ a Common Dimsor or Common Factor, Definition to be 
given. 

Note.— Too great importance can hardly be given to this exercise of in- 
spection. The application of the principle is indispensable in many of the 
arithmetical exercises in every succeeding grade. With proper training, it 
will become, within reasonable limits, a fixed mental habit, requiring no con- 
scious effort. 

Reduction of Fractions to Lower Terms or Less Denominators — 
Examples — Analysis D.. (Page 152). Definition of "Lowest 
Terms." # 

Examples in finding what part one whole number is of another 
— corresponding examples in tables. 

IV. — Multiple — term illustrated and defined. 
Common Multiple *' . ** *' 

Exercises, to be solved by inspection. 

Reduction to Common Denominator — use two fractions only. 

Application of common multiple in reducing to common 
denominator. 

Distinction between comtnon multiple and common denomi- 
nator. 

Definition of common denominator. 

" " least common denominator. 

Examples in reducing to least common denominators. — 
Analysis C. 

Examples involving previous reduction to lowest terms, by in- 
spection. Reduce f| and A to their least common denomi- 
nator. 

Use of common denominator as the simple but indispensable 
basis for the working and explanation of Addition, Subtraction, 
and Division of Fractions. 



ARITHMETIC, 149 

V. — Impossibility of adding quantities with unlike names, 
illustrated : Add 3 elms and 4 oaks ; add 3 trees and 4 trees — 7 
trees. 

In teaching the elementary principles, the subject of fractions 
should, as far as possible, be divested of technicalities, and be 
made to coincide with the acquired experience and simple 
notions of a child. 

On this account it is much better at first, to say, find | of f , 
than to say, multiply f by |, or find | times f . 

Adding things of like names. 

Adding fractions of the same denominator — Examples. 

Adding fractions of different denominators — Examples — 
Analysis C. (Page 152). ^ 

Necessity of reducing to common denominator. 

The numerators only added ; why ? 

Note.— In no example give more than two fractions. The common 
denominator to contain not more than two digits. 

Addition of small mixed numbers — Examples — Analysis C. 

Note.— See that the sign of operation and the equality sign are not omitted. 
Avoid reducing to improper fractions. 

Rule. — 1st. See that the fractions are in their lowest terms ; 2d. 
Reduce to common denominator ; 3d. Add their numerators, etc. 

Subtracting fractions of different denominators — Analysis C. 

RuU. — 1st. See that the fractions are in their lowest terms ; 2d. 
Reduce to common denominator ; 3d. Subtract the less nume- 
rator from the greater, etc. 

The same examples may be used as in addition. 

Questions should be occasionally varied by asking: "Which is 
the greater ? " or '' What is the difference ? " 

( 1st. Reducing to improper fractio.ng. 

Note.— In mixed numbers avoid •< ^d. The difficult case, 7i— 2i (deferred 

' to review.) 

YI. — " Multiplication of fractions " and '* compound fractions " 
identical. 

Such expressions as \ of 2|, f of |, etc., only involve the find- 
ing of a fractional ^^r?!, and should be treated at first as such, 
rather than as a special kind of fractions. 

It must not be forgotten hy the teacher that from the nature and 
definition of a fraction, every example in fractions must involve 
or relate to division in some way. 



150 



HOW TO TEACH 



There are two cases in the so-called multiplication of 
fractions : * 

1st. Where a fraction or mixed number is to be 
actually multiplied. In this case the multiplier must 
be a loliole number — as 3 times f , or 3 times 4f. 

2d. Where ^ fractional part is to be taken of eitlier a 
whole mmiier, or of a fraction^ or of both; as f of 17, 
or I of f, or I of 7i. 

Note.— Mutliplication by a mixed number is a combination of the 1st and 
2d cases. 

Only in the first case should the expression '•'• times " be used. 

In the second case the expression "of" only should be used. 

In the case of multiplying by a mixed number, the expression " times'''' is 
used for conciseness, though not logically correct. The proper expression is 
too cumbersome in practice — " 4 times the number and % of the number.'''' 

Only the two varieties of the first case, and the first two varieties of the 
second case should be required until the subject is reviewed. 



Examples : 
Multiplication of Fractions 



Multiplicalion by Fractions 
= taking part — division : 



7 times | Analysis as in simple 

X , tlien B. (Page 152). 

7 times 4| Analysis as in 

simple X , then B. (Page 152). 

i of 24; 41 of $24. No analysis, 
except reducing to lowest terms. 

I of 25 ; M of $25, Analysis E. 
(Page 152). 

I of ^ ; If of t. Analysis F. (Page 
152). 



For rule and its origin, see Analysis F. 

Examples to be given in the practical form at as early a stage 
as can be made expedient. 

Find how many cents, or cents and mills, in a given fraction 
of a dollar. 

Occasional examples involving preliminary reduction to lowest 
terms. 



Rule. — 1st. See that the fractions are in thetr lowest terms ; 2d. 
Multiply the numerators for new numerator, and the denomina- 
ters for a new denominator. 

Solutions by direct cancellation should not be required until the 
review. 



ABITEMETIC, 151 

VII. There are, theoretically, two cases in the Divis- 
ion of Fractions : 

1st. Division of a fractioi^^al dumber by an inte- 
gral number, as I -^ 7, and 4| -^ 7; evidently identical 
with \ of |, and \ of 4-| in the so-called multiplication 
of fractions. 

2d. Division of any number, integral or fractional, by 

A FRACTION^AL KUMBER, aS 5 ~ -J, f -f- |, 8| ^ -|, 8-| ~- 9f. 

• The form of putting the questions should be varied as much 
as possible, so as to train pupils to select and apply the right 
principle and method. Sometimes the divisor, sometimes the 
dividend, should be first named. 

" How many times are 4| contained in 9 ? '* Use this form of 
questioning at least as frequently as the more technical form, 
Divide 9 by 4|. 

The two varieties of the first case, and the first two varieties 
only of the second case, should be required before the review. 

Examples in Division of and hy Fractions — Analysis : 

The method and analysis to be by common dimsor. The first 
case may also be analyzed by Analysis F (page 152), if desired. 

The method ly inverting the divisor is deferred to the 
review. See Note 1 under Analysis G (page 153.) 

Bule.—l^i, See that the fractions are in their lowest terms ; 
2d. Reduce to a common denominator ; 3d. Divide the numerator 
of the dividend by the numerator of the divisor. 

Examples in finding what part one fractional number is of 
another. Begin with integers : 5 are what part of 8 ? 8 what 
part of 11 ? (Analyze from the unit, 1 is i of 8, 5 are f of 8, etc., 
etc.) 

I are what part off? f are what part of i ? etc., etc. 



152 SOW TO TEACH 

Practical Examples : j If 7 yards cost $f , what will a yard cost ? ) 

1st Group. "i^'Syards '' $4f, " " " " [ 

rif a yard cost $J, how much can be 

9rq Prmm J hougllt for $8 ? 

(, bouglit for $t ? 
q.! nw.,iT^ j If 8 yard cost $5, what will a yard cost? ) 

FORMS OF ANALYSIS FOR THE OUTLINES OF COMMON FRACTIONS. 

Analysis A. — Example. — Reduce 5j to halves, or to an improper 
fraction :— 1 == f ; 5 = 5 times f =^/ ; J# + i= V^. 

Analysis B. — Example. — Reduce -^/- to units, or to a mixed 
number : — 1 = f ; hence, in ^- there are as many units as \ are 
contained times in -^j equal to 7^. 

Analysis C. — Example. — Reduce | to ninths : — In a unit there 

are f ; hence \ = J, and f = 2 x f = f . 

Note.— Avoid saying "a whole number," or " one whole number," when 
speaking of a unit. 

Analysis ly.— Example. — Reduce if to its lowest terms : — By 
inspection the greatest common divisor is 6, hence it may be re- 
duced to thirds ; -p^ = i ; hence there are as many thirds as 1% are 
contained times in ||, or two-thirds — |. 

Analysis E. — Example. — Find f of 25. \ of 25 is 3i ; | of 25 are 
3 times 3i = 9f ; or (using as a basis the Axiom f of a unit = i of 
3 units ; f = -J of 3, first illustrating objectively by Hues divided 
into parts), f of 25 =: i of 3 times 25 = i of 75 = 9|. The former 
process is, in many respects, preferable. 

Analysis F. — Example. — Find f of f . (First, as a basis, show 
OBJECTIVELY that ^ of i = i ; 2 of i = :^ ; 4 of i = i^-, etc., etc.) 
1 of I zr: ^8 ; i of f = 5 timcs ^ = A ; f of ^ == 3 times ^ = if. 

Note 1st.— Make the same question "practical," and apply the same 
analysis. If a yard cost $y, how much will f of a yard cost ? It will cost | 
of f of a dollar, etc., etc., as before. 

Note 2d. — After a few simple examples have been carefully analyzed, 
point out the numerical relation of the numerator and the denominator of the 
product to those of the factors, and theriy not before, deduce or give the follow- 
ing 

Bule for the Multiplication of Fractions : 

1st. See that the fractions are in their lowest terms ; 2d. Mul- 



/' 



ABITHMETia 153 

tiply the numerators for the numerator of the product; and 
multiply the denominators for the denominator of the product. 

Analysis G. — Example. — If a yard costs $f , how much can be 
bought for $J ? 

(See Analysis B, 5th Grade, to be combined with reduction to 
Common Denominator.) 

If a yard cost $i, $J will buy as many yards as $f are con- 
tained times in $J, or, reducing to Common Denominator, f = 
fl, 5 = f f , as many yards as f J are contained times in f f , or 2-ir 
yards. 

Note 1st.— To "invert the divisor and proceed as in multiplication," is 
much more concise as a method, but it is not in any sense an analysis^ but a 
condensed and valuable rule^ which is to be both taught and analyzed in the 
review. When this concise rule is taught before the analysis by reducing to 
a common denominator, the teacher will usually find three undesirable results: 
first, the pupils are as likely to invert the wrong fraction as the right one, 
unless the question is always put in one particular way, and even then, until 
after much practice ; thus showing that they are not guided by any principle : 
second, they cannot explain the process ; and third, it is then much more 
difficult to teach the analysis, because their minds are preoccupied by the 
brief rule, which naturally seems to them so much more desirable, as it costs 
little or no mental efibrt. 

As the study of fractions is an important luental discipline, any course 
which practically excludes the fundamental principle of division by a fraction 
should be carefully avoided. 

Note 2d.— It will be perceived that the analysis of the division of one frac- 
tion by another by the process of reducing to a common denominator, is essen- 
tially identical with the analysis of reducing an improper fi-action to a whole 
or mixed number. 

Analysis H. — Example,— If^ f of a yard cost- $f, what will a 
yard cost ? 

(See Analysis C, in 5th Grade, with which the following is es- 
sentially identical.) 

If ^ of a yard cost $f , | of a yard will cost \ of $f (note that this 
division by the numerator is the vital step in the process), which 
is $/o- ; and a yard or \ will cost 7 times $/o, or $|J, equal to %1-io. 

Note 1st.— This is one of the most important analyses in the entire range 
of the arithmetic of the grammar-school grades. If neglected, or badly taught, 
it seriously deranges the work of the teachers of more advanced grades, where 
it must be so frequently applied. If the teacher will present it immediately 
after^ and then in connection with, a review of Analysis C, in the Fifth Grade, 
and dwell particularly upon the step noted in parenthesis, sl great part of the 
difficulty in fix:ing the entire process will disappear. 



154: HOW TO TEACH 

Note 2.— It is, of course, understood that the examples given to the class 
will not be confined to yards and dollars. Even the order of these should be 
at times inverted ; as, in the problem last treated, we might have — 

If $5 purchase f of a yard, how much will a dollar buy ? 

Syllabus op Topics for Expanded Review of Commok 

Fractions. 

I. Systematic Bemew of Definitions of terms used in fractions, 

with illustrative examples. Omit complex fractions having fractions 

in the denominator. Complex fractions having an integral de- 

2- 
nominator, such as -^, read 2^ fifths, are to be *' reduced to higher 
o 

terms." See Analysis C, page 152. The multiplier to be used is 

evidently the denominator of the fraction found in the numerator. 

All other cases of " complex fractions," so called, should be 

treated as indicated division. Such expressions as — are not 

to be explained as fractions. A unit cannot be divided into 9J 
equal parts. 

Examples in finding the Greatest Common Factor of numbers by 
inspection. — Mental. 

Examples where the factor cannot be readily found by inspec- 
tion, as 292 and 365 ; — 315 and 572. The special method re- 
quired is too difficult for analysis in this grade. It is one of the 
few points to be taught empirically. 

The result always should be tested or proved in accordance 
with the definition of Common Factor or Common Divisor. 

II. Beduction of Fractions to their Lowest Terms. 

Examples to be reduced by inspection ; il8J, ff o> Analysis D, 
page 152. 

Examples involving the special method of finding the Greatest 
Common Factor ; as |||, f }f , etc., etc. Not too long. — Analysis 
D, page 152. 

Beduction of Improper Fractions and Mixed Numbers, 

1st. Examples solved mentally or by inspection. 
2d. Examples with larger numbers. — Analyses A and B. 
Examples in finding the Least Common Multiple of two or 
more numbers — and definition. 



ARITHMETIC, 155 

1st. By inspection, as 5, 3, 2 ; 10, 20, 30. 

2d. When not readily solved by inspection, as 28 and 39 ; 72, 

25, 88 ; 6, 12, 18, 24, 36, and 48. 

Statement of Metliod or rule. 

Relation of Least Common Multiple to Least Common De- 
nominator. 

Distinguish carefully between the two, and define eacfi. 

Examples in reducing to Least Common Denominators. — 
Analysis C. 

Give occasional examples involving preliminary reduction to 
lowest terms by inspection. 

III. Analysis C. Examples in Addition of Fractions and of 

Mixed Numbers, 

Say ^y Reduce to Least Common Denominator P r2i\hQV than, ^^Find 
the Least Common Multiple of the Denominators. Of course the 
latter forms a part of the process of the former. 

Examples in Subtraction ; as -h — A" ; 871 — ^29if . Do not allow 
reduction to improper fractions. 

Make both kinds of examples as practical as possible. 

Practical Examples (not too long), each involving both addition 
and subtraction. 

Note.— Teachers shoalcl remember, that arithmetic is not only a science^ 
but also a practical art ; that this art involves important devices, many, or 
most, of which have been already taught, and their principles explained. 
These devices, such as reducing to lowest terms, cancellation, rejecting ter- 
minal O's of a divisor, should not be at any time lost sight of. Examples 
should be occasionally given of such a character as to require these devices. 
The omission or neglect of these important matters would be a serious defect 
in the character of the instruction given. 

Principle of Cancellation. — Show its identity with dividing by 
common factors^ and with reducing to lowest terms. Show this by 
examples in fractions. 

Examples of simple applications of cancellation to whole 
numbers. 

IV. Multiplication of Fractions 

Give examples ' where cancellation cannot be applied. — 
Analysis F. 

tI X 3-2^; X If ; iJx 144; 16|xl2|; abstract and ^rac^eca?. 

Give examples that should be done by cancellation. — Analysis, 
Lowest terms. 



156 HOW TO TEACH 

125 X T^ ; It of $17.38 ;— if 39 barrels cost $84, what will 26 
barrels cost ? ' 

If a ton of hay cost $17i, what will f f ton cost ? 

If 1 acre cost $23y, what will 19-iV acres cost ? 

Pupils should be made familiar with the following principle 
and its applications. It is frequently the most convenient 
method of solution. See Analysis E, page 152. f of a number 
are equal to i of 3 times the number, etc., etc. 

f of40=:iofatimes40. 

V. JDimdon of Fractions, 

1st. Review and apply the method by common denominators, 

2d. Eeview thoroughly its analysis. Analysis G, page 153. 

3d. Teach carefully the following analysis, giving a variety of 
short examples to fix it thoroughly. See Analysis I, page 157. 

4th. Teach the brief and useful device of inverting the divisor^ 
but in no case let the analysis of the rule be forgotten. Let it be 
given by the pupils as often as may be found necessary to insure 
its retention. The teacher is again reminded of the importance 
of the proper application of the principle of repetition of mental 
effort. 

Examples in finding what part of one number is of another ; 
as 74 are what part of 9i ? $4|, what part of $7| ? i J what 
part of If ? — See Analysis I, page 157. 

Give examples where cancellation cannot be applied : 

11 _i_ 2 5. . 1 Ql ^ 1 2 
33 ^^ 49 » -'^"3 ^^ ^1- 

At $lf a yard, how many yards can be bought for $13J? 

If 5| bushels cost $18f, what will 1 bushel cost? 

Give examples where cancellation is to be applied : 
234-r.l2-A-;21f-^2H, etc. 

Give short examples involving simple combinations of the 
multiplication and division of fractions ; also addition or sub- 
traction, with multiplication or division, like the following : 

Bought 7| yards and 'di yards at $1| a yard ; what ts cost of 
the whole ? 

Bought 36 yards ; kept 9|- yards, sold the remainder at $f a 
yard ; how much did I get for it ? 

If I had sold it for $74, how much a yard would that be ? 

If § yard cost $?-, what will A yard cost ? 

If I yard cost $f , how much can be bought for $5| ? 



ARITHMETIC. 157 

Forms op Analysis. 

The following is the simplest form of the analysis of the im- 
portant practical rule of ** inverting the divisor/' etc. The in- 
troductory step of using a unit as the dividend, is only a case 
of dividing one fraction by another. 

Analysis I.— Example,— DWi^Q I by f-. 

{Begin with a unit for the dividend^ and apply the principle of 
common divisor,) 

1st Step.— A unit divided by f , or ^ -r- f = J (which quotient, it 
will be observed, is the divisor inverted), 

2d Step.— Therefore | of a unit divided by f = | of f = J^. 

Condensed form.—(l -f- f ) = (?^ H-f ) = i ; therefore (| -v- f ) = f 

ofi=fi. 
Example,— If f of a yard cost $|, how much can be bought for 

Analysis. — Combination of H and G. Page 153. 
Example,— If ^ of a yard cost $f. what will A of a yard cost? 
Combination of H and F. 

Note.— Give a thorough review of analyses F, G, and H, before attempt- 
mg the above combinations. 



Decimal Fractions. — ^The exact nature of decimal 
fractions should be explained and illustrated ; also the 
meaning of the word decimal Show that decimal frac- 
tions may be used like common fractions by writing 
the denominator. Illustrate by the decimal notation, 
showing that whole numbers greater than 9 are also ex- 
pressed decimally. 

Show also that decimal fractions are really only a 
kind of common fractions, the two having the relations 
of species and genus. The methods of writing, and tlie 
various analyses are essentially identical, case for case, 
as shown by the following syllabus. * 



158 SOW TO TEACH 

The illustrations may embrace the following : — 1. 
How to write decimals, as 7-tenths, 7-hundredths, 7- 
thousandths, 7-ten-thousandths, etc. 2. Show that the 
numerator is first written, as in common fractions. 

3. Show that the ^'decimal point ^' and the ciphers, 
when used, are only required to indicate the denominator. 

4. In reading decimal fractions, the pupils should be 
cautioned to avoid such expressions as " tens of thou- 
sands ^^ for ten-thousandths^ " hundreds of thousands " 
for hundred-thousandths^ etc., etc. In connection with 
the reading of such fractions, pupils should be trained 
to recognize readily the comparative value of different 
fractions; as that .3 is greater than .0987 or .01 than 
.009596, etc. They may also be made to perceive readily 
the approximate value of decimals as compared with 
simple common fractions ; as, that .7634 is a little more 
than I ; that .8741 is somewhat less than f , etc. Pre- 
vious to this, however, it is well to teach the exact value 
of certain decimal expressions: as .75 =|, .125 = -J-, 
.375 — |, etc. These exercises will serve to render the 
subsequent work of the pupil intelligible. 

Syllabi: s of Topics. 

I. Exercises in keading decimal fractions. 

Exercises in telling how many places are necessary for a given 
denominator, and we versa. 

Exercises in writing decimal fractions. 

Reduction of decimal fractions : 

1st. By Inspection, with analysis as in common fractions. 

Examples, mental, oral, and written. 

.3 to .OO's, to .OOO's, etc. ; .15 to .OOOOO's. To higher terms. 
Analysis C, common fractions. Page 152. 

3 to .O's, to .OO's, to .OOO's, etc. ; 7.3 to .O's, to .OOO's, etc. ; to im- 
proper fractions, Analysis A, Page 152. 

Reduce . 700 to lowest decimal terms. Give Analysis D, Page 152. 



ARITHMETIC. 159 

Note.— Avoid saying "the ciphers to the right are crossed off because 
they are of no use^ The statement that " they do not affect the value," is 
not satisfactory unless the pupils show why they do not. 

II. Reduce common fractions to decimal fractions. Give Analy- 
sis E. 

Use axiom — f of a unit = i of 3 units ; J =: ^ of 3. 

Make this definite by objective illustration, using lines divided 
into parts. 

Example. — f to tenths ; to hundredths ; f of 1 = ^ of 3 = i of 30 
tenths = 7i tenths = .7i = .75. 

Note.— Pupils should be accustomed to read decimal fractions, especially 
hundredths (in subsequent grades applied to per cent.), so as to include out- 
etanding fractional parts, where there are any. 

It is generally better to state what denominator is required, instead of the 
more indefinite requirement to ''reduce to a decimal fraction." 

Example.— UQdxkCQ -,^i- to a decimal fraction of two places, or reduce i^f 
to hundredths. 
Am. Two places will give hundredths for the denominator. 

4 1 1 \4.00 

— = — of 4 = — of four-hundred hundredths = 11/ 

11 11 11 .36 4-11 

240 240 24 3 \3.00 

Ijeduce — to a decimal : — = — =- = Kof3 = ^of 300 hundredths =4^ 

320 320 32 4 .75 

Rule 1. 1st. Reduce the numerator, considered as a whole 
number, to an improper fraction with the required denominator. 
2d, Divide by the given denominator. Or, 

Rule 2. Dimde the numerator by the denominator. 

Note.— Give examples to show what common fractions in their lowest 
terms can he made entirely decimal, and which can not. In the general work 
of the class, pupils should rarely be required to continue the division 
beyond three or four places. 

Reducing Decimal Fractions to Common Fractions in their 

Lowest Terms. 

Rule.—'WniQ the fraction as a common fraction and reduce to 
lowest terms. Analysis D, common fractions. 
Examples: .^2^ .4125 .87500 14.125 

.071 .3i .661 5.1U .87i 

Note.— Pupils should be made thoroughly familiar by rapid mental exer- 
cise, usually without analysis, with the decimal expressions for halves, 3ds, 
4ths, 5ths, 6ths, 7ths, 8ths, 9ths, llths, 12th?, and vice versa, using preliminary 
reduction to lowest terms whenever possible, as in -^%, J, etc., etc. 



160 SOW TO TEACH 

III. Addition of Decimal Fractions, 

Examples: Add .2, .05, .008, .7283. Add .0005, .97, .0101, etc. 
" Give mixed numbers. 

Analysis as in common fractions, by principle of reducing to 
lowest terms. The necessary additional ciphers may be '' under- 
stood " in the solution, but not in the oral analysis, which should 
be as brief as possible. 

IV. Subtraction of Decimal Fractions. 

Examples : .1 — .075 ; 1.001 - .01009, etc. 

Explain as in common fractions, with the same analysis. 

V. Multiplication of Decimal Fractions, 

Note.— Do not give large denominators. Use the b?i,e/ rule of common 
fractions. Cases as in common fractions. 

1st. When a fraction or a mixed number is to be multiplied, as : 
4 times .75, 17 times 8.047. 
Value of 13 barrels at $8,375 a barrel. 

2d. When a fractional part is to be taken, as : • 

.4 of .83, .4 of 75, .4 of 8.75. 

How much is .7 of $38.45 ? .079 of $120 ? .90^ of $160.48 ? 

Value .179 of ton @ $92 a ton ? at $92.87>^ a ton ? 
3d. Combinations of the 1st and 2d cases, as : ' 

3.4 lbs. at 79 cts. a lb. ? $.79 x 3.4. 

8 cwt. 75 lbs. ® $2.47 a cwt. $2.47 x 8.75. 

Note.— As preliminary to 2d and 3d cases, give mental exercises in finding 
the product of two decimal denominators, as " lOths by lOths, how many 
places ? " " lOOOths by lOOths, how many places ? " etc., etc. 

Examples of cases involving reduction : 

.024 X .15 = ? Product of numerators, 24 x 15 = 360, the new 
numerator, lOOOths by lOOths = lOO.OOOths, or 5 decimal places 
for denominator. Ans. .00360 = in lowest decimal terms .0036. 
Why cross off the last ? To divide both terms by 10. 

Note.— Many questions are as well solved by the application of principle 
(E) in common fractions. See Analysis E, page 152. 

.079 of $14.83=. 001 of 79 times $14.83, etc., etc. 
Use or not as may be judged expedient. 

VI. Division of Decimal Fractions, 
There are two cases, as in common fractions : 



ARITHMETIC, 161 

1st. When the divisor is an integer : 

7 ^ 8, 8 -^ 7, 6-^5, 6 -^ 120, 7.2 -i- 6, 3.6 -^ 120, etc. Put ques- 
tion in several ways : 1st, Divide 7.2 by 6; 2d, How much is 
^ part of 7.2 ? 3d, How many times is 6 contained in 7.2 ? 
etc., etc. 

This simple case does not require the principle of the common 
denominator. 
2d. When the divisor is or contains a decimal fraction : 

6 -^.03 ; .8 -J- .005 ; .004 -- .8 ; .0036 -f- .024 ; 7.2 -r- .009 ; 8 h- 5.45 ; 

3-5- 7.203 ; .2 -r- 8.75 ; .3006 -5- 7.4 ; 8.5 -f- 9.78; 8.638 -h 9.5 ; 8.638 

-7- 4.3, etc., etc. 

Solution and analysis by the principle of common denominator. 

There are two forms of applying this principle : 

1st. Where the denominator of the divisor is the greater^ 
(.003). 6,) INCREASE the denominator of the dividend to .OOO's. 

2d. Where the denominator of the divisor is the less, (.12).1 7286, ) 
DIMINISH the denominator of the dividend to .OO's (hundredths) 
by cutting off the last three figures. 

A General Bule. — 1st. Reduce the denominator of the dividend 
to the denominator of the divisor ; 2d, Divide the numerator of 
the dividend by the numerator of the divisor. 

The quotient will then be a whole number. Other decimal 
places either added to the dividend or cut off from it, are to be 
** brought down " in the further division, and Will give the frac- 
tional portion of the quotient. 

Applications. — The applications of decimal fractions will be 
principally found in Federal Money. Simple combinations with 
common fractions should occasionally be used ; also simple com- 
binations of two or more of the rules of decimal fractions. 

Use the ^vmoX^lQ^ oi cancellation diXid. reduction to common frac- 
tions whenever they will simplify the operation. 

Examples in finding what decimal fraction one decimal fraction 
is of another ; especially how voi'djij hundredths— u^q only small 
amounts or very simple examples : 

8 cents, how many hundredths of 64 cents ? 
$7.25, how many hundredths of $9.75? 



163 HOW TO TEAGH 



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QEOGRAFEY, 163 



GEOGRAPHY. 



OeograpTiy of the United States in detail. — Ik teach- 
ing the geography of the United States, it is particularly 
important that the time of the pupil be not exclusively 
taken up with the study of mere local details — with 
learning the several courses, etc., of long lists of rivers, 
and the exact situation of still longer lists of towns. 
A certain, but carefully limited, amount of local geo- 
graphy is indispensable as a basis for the more im- 
portant descriptive geography. 

The necessary local geography embraces the names of 
the several States and Territories, and their division into 
several groups, as New England, Middle, States etc., etc.; 
their boundaries or relative positions ; their important 
rivers, lakes, bays, capes, islands, mountain ranges, and 
peaks ; the capital of each State, and a few of its other 
leading cities or towns, if of any importance. All these 
should be carefully learned as a basis for the subsequent 
portions of the study. 

The descriptive geography should include the simplest 
physical outlines of the country as a whole ; the eleva- 
tions^ the great mountain ranges, plateaux, and plains; 
the drainage by single rivers on the Atlantic slope, and 
by extensive complex river systems in the remainder of 
the country ; the climate^ with its modifications in the 
several sections, as cold or hot, wet or dry ; the leading 
industries and the staple agricultural, mineral, and 
manufactured productions, with their dependence upon 
the physical conditions. 

Add to this a simple and very brief outline of the 
general and State governments, the population, its four 
races and their distribution; the great commercial 



164 . HOW TO TEACH 

routes, natural or artificial, and the cities, as the centers 
of manufacturing and commercial industry. 

The. descriptive geography of mdividual States or 
Territories may then, in great part at least, be deduced 
from a consideration of these general facts. All tire- 
some sameness and repetitions will thus be avoided, and 
the pupil will be made to appreciate the real importance 
of the study. 

ELEMENTARY SCIENCE. 

(By Oral Instruction.) 
BOTAKY. 

The general suggestions relating to the object of this 
branch of instruction, given in connection with the 
subject of zoology, in the preceding grade, and the re- 
marks there made in regard to the exteat of classifica- 
tion, the terms employed, etc., are equally applicable to 
the subject of botany. As a science of observation, this 
subject has a decided advantage over zoology, especially 
for educational purposes, inasmuch as the objects of 
which it treats are examined, dissected, and analyzed 
with more facility. They also possess more obvious 
beauty, and are devoid of the repulsiveness which at- 
taches to so many objects of the animal kingdom. An 
insect, apparently disgusting at the -first view, when 
closely examined, often shows more beautiful properties 
and more striking evidences of design than the most 
elegant blossom ; but the natural aversion to handle it, 
or come in contact with it, must first be overcome. 

The classification of plants, being based upon dis- 
tinctions often very minute, must, for the purposes de- 
signed to be accomplished in these simple lessons, be 



ELEMENTARY SCIENCE. 165 

carefully limited. Only common plants need to be 
classified. The limitations of the classification to be 
taught are indicated below. 

The first feio lessons should show the structure of 
plants and the general functions of each of their parts, 
— the rooty the stem, the leaf, the floiuer, the seed ; the 
growth of the plant from tjje seed, both as to root and 
stem, the food of plants, buds and branches, — how a 
plant grows from them ; the distinction between lierhs, 
shrubs, and trees ; also between annuals, biennials, and 
jjerennials. Examples of each to be given. 

Classification of leaves — a beautiful and very useful 
department of the subject, especially as a means of 
training the powers of observation — may then be 
taught, the qhildren being encouraged to gather speci- 
mens for careful scrutiny. The vocabulary employed 
to indicate the peculiarities is very interesting, and will 
serve to teach something of etymology — as ovate, cordate, 
palmate, digitate, serrate, etc., etc. Give the pupils /or- 
mulce for methodical examination and description. 
{See Miss Youmans^s "First Booh of BotanyT) 

Classification of roots and stems, to be taught in a 
similar manner, but much more briefly. Next, that of 
blossoms. First, show the parts of a blossom, taking a 
regular one to begin with — as of a lily^ a morning- 
glory, or a butter-cup. Analyze so that the pupils can 
see the parts, showing the calyx and sepals, the corolla 
and petals, the stamens and the pistil with its ovary. 
Give a sufficient number of exercises to make this fami- 
liar, and let the pupils analyze for themselves. The 
principal forms' oi fi^ov^QY^, as bell-shaped, 'wheel-shaped, 
salver-shaped, cross-shaped, butterfiy-shaped, etc., etc., 
may then be shown. The arrangement of the blossoms 
on the stem (inflorescence), as far as it can be exempli- 



166 HOW TO TEACH 

fied by actual specimens, as head, raceme, spike, iimlel^ 
etc., may also be learned. 

The following outline of classification may be 
taught : — 

A. (Series.) Flowering {lohcenogamous) plants. 

B. (Series.) Flowerless {cryptogamous) plants. 

At first use only the familiar terms. The scientific 
may often be dispensed with entirely. Give examples 
of plants in each series ; as — 

Rose, Lily, Geranium ; Fern, Moss, Mushroom, 

A, including a (class). Outside-growing {exogenous) 

plants 
h (class). Inside-growing {endogenous) 
plants. 

Illustrate by stems, showing the rings or annual lay- 
ers of growth in the former, with larh, tuood, emdijnthy 
and their absence in the latter. Teach the coincident 
peculiarities of the leayes, as netted-veined and parallel- 
veined, aflbrding a ready method (approximate) of dis- 
tinguishing these plants, and thus giving opportunity 
for useful exercises ; also those of the seeds, as of two 
seed leaves (cotyledons) or only one {dicotyledonous 
and monocotyledonous). 

Familiar examples to be found by the pupils ; such 
as Kose, Buttercup, Geranium, Pea, Potato, Grape-vine, 
etc., etc., and Lily, Indian Corn, Common Grass, etc. 

{a). Including 1. Orders or families of plants, with 
blossoms of many petals {polypetalous) ; and, 2. Orders, 
or families, of those, with blossoms of one petal {mono- 
petalous). The pupils will readily find specimens of 
each, the names of which they have already learned. 

The orders of {I) should not be taught. Nor need 
any instruction be given in relation to the classification 
of cryptogamous plants, ferns, mosses, etc., this being 



ELEMENT AR T SCIENCE. 167 

too difficult, and depending npon distinctions not suffi- 
ciently obvious for the purpose of these lessons. Atten- 
tion, however, may, if occasion offers, be called to the 
fructification of ferns. 

Such of the orders or families, should be taught as 
are very familiar, and depend upon quite obvious dis- 
tinctions, familiar names being exclusively used. Thus 
the Mustard Family, the Pulse Family^ the Croufoot 
Family, the Rose Family, the Lily Family, etc., etc., 
may be taught as far as the collection and presentation 
of specimens render it desirable ; that is, not the mere 
fact that there are such families, but in connection 
with an actual object, and when the inquiry is, to what 
family does it belong ? If the season permits, and there 
is an opportunity for the pupils to seek for specimens, 
this part of the instruction may be extended. Here the 
judgment of the teacher (never to be superseded) must 
be carefully exercised, it being constantly in view that 
the object of these lessons is not to make the pupils 
hotanists, but to create a basis for the study of natural 
objects, and to develop the faculties of perception and 
reflection. Species need not be taught, although the 
pupils may, as occasion offers, be made to perceive the 
diversity presented by different individuals of the same 
family, so as to learn what is meant by species. 

The common uses of plants may be taught to some 
extent incidentally with some of the above instruction, 
but more fully at this stage. This will embrace their 
uses for food, clothing, medicine, etc. Take our own 
plants first. Show that the roots of some plants are 
useful; of others, the 5e6c?6' ; ot\iQYB,i]iQ leaves; others, 
the fricit ; others, the iai^Jc, etc. Some few plants of 
other climates and countries may then be referred to, 
as cotton, rice, sugar, tea, coffee, etc., etc. The relation- 



168 BOW TO TEACH 

ship of these plants to our own may then be shown; 
that is, the families to which they belong. 



MINEEALOGY. 

Before commencing instruction in this branch, the 
teacher should again read the general remarks on teach- 
ing elementary science in the Fifth Grade. This sub- 
ject presents some peculiar advantages for attaining the 
special object of oral instruction — the discipline of the 
observing faculties. In no other department of natural 
science, is it so completely within the power of the 
teacher to present the facts to be acquired to the im- 
mediate perception of the pupils in the class-room, and 
in no other is more delicacy of discrimination required 
in the exercise of the senses upon which the perceptions 
are based. But while the objective metliod is thus seen 
to be peculiarly applicable to this branch of science, it 
must, at the same time, be remembered that no other 
subject perhaps requires so large a share of imparted 
information. This, however, should be given not arbi- 
trarily, but as something needed- to supplement the 
knowledge gained by the pupil in the exercise of his 
own faculties,. and, as far as possible, in answer to his 
inquiries, the determination of the mind to self-activity 
being the great desideratum in this kind of teaching ; 
hence, the important principle should be kept steadily 
in view that nothing should be done for the pupil which 
he can be made to do for himself. . 

The teacher should also bear in mind that it is utterly 
impossible to teach the subject without special i^repara- 
Hon for it — without being practically familiar with at 
least the outline facts of the science. This preparation 
may readily be made with the assistance of even a small 



ELEMENTARY SCIENCE. 169 

cabinet of minerals, properly labeled {Day^s Grammar 
School Cabinet^ for example), and any of the smaller 
manuals of Mineralogy (Dana's, for instance). 

What has been said in the preceding grade, as to the 
propriety or necessity of attempting only a part of the 
subject, is equally applicable here. What is done should, 
however, be systematic — not miscellaneous and unre- 
lated. Do not attempt to treat any of the topics ex- 
haustiyely. A large part would not be understood or 
remembered, and valuable time would be misapplied. 

The investigations made by the pupils in relation to 
each mineral should be guided by the teacher by means 
of a regular formula, considering in a fixed order its 
form, structure, cleavage, fracture, hardness, weight, 
color, luster, etc., etc. These special characteristics and 
their proper order will be readily remembered after a 
little practice. Each term thus used should be care- 
fully illustrated and explained as soon as its introduc- 
tion becomes necessary. 

Begin with Minerals— Rochs to be afterwards con- 
sidered as mineral aggregates. A clear conception of 
the general properties of minerals may readily be given 
by commencing with ice — water — steam. 

As a preparatory step, lead the pupil to form some 
definite idea of the variety of forms of crystals, by briefly 
comparing coarse salt, alum, borax, quartz, mica, rock- 
candy, etc. Use only the term crystal, without giving 
the names of substances. 

In treating of ice, draw attention, not by telling, but 
by proper questioning, to its transparency, color, luster, 
weight, solidity, hardness, fracture, and to the needle- 
like crystals which can be so readily shown in ice-films 
when water begins to freeze, and in the frost-flowers on 

the window-pane. Lead him now to see that a block of 
8 



170 J^OW TO TEACH 

ice, or a snow bank, must be made up entirely of such 
crystals, even tliough their indiyidual fornis are no 
longer perceptible. Show next that many other fluid 
substances, like water, upon losing their heat, crystallize 
into definite solid forms, under favorable conditions, as 
in melted sulphur, and in the beautiful zinc crystals 
which cover the surface of so-called galvanized iron. 
Dwell somewhat upon these phenomena of crystalliza- 
tion, and draw attention to the mysterious and inde- 
structible force which somehow rebuilds the atoms of 
the water into the same forms, no matter how often the 
ice may be melted. 

The next step in this preliminary lesson will be to 
show that crystals may also be formed from substances 
in solution. Alum, salt, borax, etc., will furnish ready 
means of illustration. Lead the pupil further to 
notice, that, as in the case of the ice, so with the sulphur, 
zinc, alum, etc., the crystals may become so massed as to 
be no longer individually distinguishable. 

The principal points to be fixed in sucli a lesson are 
that there are many kinds of crystals, some formed from 
liquids which have become solid by a loss of heat, and 
others deposited from solution. These facts will be found 
of great importance in further treating the subject. 

The pupil is then prepared to compare ice with a 
quartz crystal, which should be presented but not at 
-first oiamedj and should be compared first as to the re- 
semblances, then the differences. When the pupils can 
be made to furnish no more ideas, the teacher should state 
where it is found, its relative abundance, geological im- 
portance, economic uses, etc., etc. Be particular not to 
introduce an unexplained term — such as the name of any 
rock or mineral, as gneiss, or gypsum. The name means 
nothing until explained as quartz has been. Other forms 



ELEMENTARY SCIENCE. 171 

of quartz may then follow, each, treated in the same way, 
and each in its turn compared with those that have pre- 
ceded it. This will constitute an excellent review, and will 
thoroughly fix what has been already taught. Encour- 
age the pupils to look for and bring in specimens which 
they think to be of the same character as those studied. 
Let tliem tell why they think they are the same. Let 
others tell why they think they are not. 

Having thus treated of quartz, next consider, in the 
ssime waj, feldspar and ^nica. The pupils will now be 
ready to consider a rock. 

Let it be gneiss or granite. Let the pupils look for 
the minerals in it [a cheap single lens as a magnifier 
will often be of service]. Then consider the texture, 
structure, where found, uses, etc. The mineral /^on^- 
hlende and its important varieties may then follow, and 
after that the rock syenite. 

All needful information may be obtained from any 
of the manuals in use. 

It will not be necessary here to follow out in detail all • 
the minerals and rocks of which it is desirable that pupils 
should have some knowledge. A list of the more impor- 
tant, mostly from Dana, is subjoined, from which the 
teacher can make such selections as will conform essenti- 
ally to the above plan. 

Mi:n:erals. 

Water; carbon, diamond, coal and coal-mining, an- 
thracite, bituminous, jet, plumbago, amber, petroleum, 
asphalt; sulphur; saltpeter, salt, borax ; lime, gypsum, 
alabaster, selenite, calcite spar, chalk, stalagmites, lime- 
stones (crystalline and compact), marbles, quicklime, 
hydraulic lime, dolomite; alum; talc, soap-stone, 
(French chalk), meerschaum, pyroxene and hornblende^ 



172 ^OW TO TEACH 

corundum and emery, feldspar, albite, orthoclase, gar- 
net, mica. 

Metals. 

Mineralized [ores] or native — Ores of tin, iron, 
nickel, zinc, lead, mercury, copper, gold, silver, plati- 
num. Enter into no details of Metallurgy ; a few sim- 
ple facts in regard to smelting, fluxes, etc., will not be 
out of place. The economic uses of these metals and 
the poisonous properties of some of them should receive 
very careful attention. 

Rocks. 

As single minerals — example pure limestone. As 
compounds — granite or conglomerate. Rocks as crys- 
talline and uncrystalline, stratified and un stratified, 
aqueous, igneous and metamorphic. 

The relative position of important rocks — granite, 
syenite, gneiss, mica-slate, steatite, trap, basalt, lava, 
j)umice, slate, shale, schist, quartz-rock, burr-stone, sand- 
stones, grits, conglomerates, limestones, marbles, sand, 
clay. 

Such of these rocks as are found in the vicinity of the school, 
or are frequently seen by the pupils when used for paving, flag- 
ging, building, etc., should receive particular attention. 

WRITING. 

Penmanship and Slate- Writing. — Pen- 
manship should be carefully taught in each grade of the 
Course, in addition to the constant practice which is re- 
quired in slate-iuriting. By means of the latter, if a due 
attention is given to it, much may be accomplished in 
aiding the pupil to acquire readiness and fluency in the 
exercise of this art; but if he be allowed to fall into 



WRITING. 173 

careless habits, his style of writing, both with pen and 
pencil, will be almost incurably vitiated. . 

The exercises in spelling from dictation, etc., should 
be performed with punctilious accuracy, even if some 
sacrifice of rapidity be at first required. Of course, there 
should be a constant efibrt to improve both in rapidity 
and accuracy — quantity as well as quality being made 
a criterion of merit and success. 

The slate-writing should, as far as it is practicable, 
exemplify the principles and methods formally taught in 
the lessons in Penmanship. Pupils should not be per- 
mitted to violate in the one class of exercises the rules 
and precepts taught and practiced in the other. This 
caution is especially applicable to the holding of the 
pencil, which should be sufficiently long to be held as 
a pen. 

The lessons in penmanship should be methodical and 
progressive, whatever system may be employed. In this, 
as well as the preceding grade, the exercises should be 
rudimentary, but the pupil should be advanced as fast 
as possible. He should be permitted to write as much 
as is practicable, — making strokes and curves is not 
writing, although it may be valuable as leading to it. 
A few of such exercises will suffice. 

Neither should the use of trial papers be carried to 
the extreme of withholding the pupil for a considerable 
time from the use of his copy-book, so that months are 
required to finish the latter. The pupil should be 
taught the necessity of doing everything as well as he 
can do it ; but perfection in details should not be ex- 
pected in the rudimental stages. It should, frora the 
first, be deemed essential (at least meritorious) to exe- 
cute the work prescribed with dispatch, provided there 
is no want of care or attention. Festina lente, however. 



174 irOW TO TEACH 

is a motto that applies to tlie acquisition of this art, as 
well as others^ in its first stages. 

A proper distinction should be made between the 
lessons given to show the pupils how to write and the 
exercises designed to practice them on what they have 
thus learned. In the former, the whole class should 
inyariably be occupied in the same work, the teacher 
explaining and illustrating from the blackboard the 
principles and methods which form the subject of the 
lesson ; in the latter, practice being the object in view, 
it is not so essential that all the pupils should be doing 
the same thing at the same time, although even here 
it is a conyenience to the teacher, since it facilitates 
supervision. 

It should be carefully kept in view that the hand and 
the eye as well as the mind oi the pupil are to be 
trained in this branch of instruction, — the hand to exe- 
cute, the eye to discern, the mind to judge. These are 
not to be educated separately and successively, but 
simultaneously. The pupil must be taught to know 
what is the correct form of every letter, and his hand 
must be so trained by correct practice, that it will exe- 
cute the dictates of mind and eye. 

Hence a correct method of holding the pen, a proper 
position of the body while sitting at the writing-desk, 
and a suitable placing of the book or paper, are all in- 
dispensable pre-requisites to the acquisition of a good 
hand-writing. The first of these demands especial at- 
tention, and every lesson should, for some time, be 
introduced by distinct directions as to the proper me- 
thod of holding the pen, and these the pupils should 
not be permitted to violate. With regard to the latter 
— position of body and position of book — a few simple 
directions will be all that are requisite. 



THIED GEADE. 

OUTLIKE COURSE. 
Time cdlowed^ from eight to ten morithi. 



LANGUAGE. 

heading. — Of the grade of a Fourth Reader, with attention 
to the elocutionary principles^ rules, and exercises required to 
teach expression; also special exercises in weal culture. 

Spelling,, — From the reading lessons, with additional exer- 
cises, both oral and written ; careful attention to syllabication. 

Definitions. — In connection with the reading lessons ; also 
a review of the pi'eflxes and suffixes taught in the preceding 
grade, and exercises in their combination with various easy- 
roots. 

EnglisJi Crrammar and Composition. — Continued, 
with the analysis, parsing, and construction of easy complex and 
compound sentences ; also the writing of short compositions 
under the inspection of the teacher. 



ARITEBIETIC. 

MentaZ Arithmetic. — Through denominate numbers and 
fi'actions, with their practical applications ; also a review of the 
preceding grades by exercises in both calculation and analysis ; 
and a careful review of the tables. 

Written Arithmetic. — As far as in mental arithmetic, with 
similar processes and methods of analysis; also with exercises 
to give practical expertness in simple computation. 



176 b:ow to teach 



GEOGRAPHY AND HISTORY. 

Geography, ^Of South America and Europe, both local and 
descriptive ; the topics of the preceding grades to be occasion- 
ally reviewed in outline. 

History.— Of the United States, including an account of the 
early discoveries, and the outlines of the Colonial History to 
1763, only such dates to be taught as are essential to a clear un- 
derstanding of the narrative. 



ELEMENTARY SCIENCE 

(for oral instruction.) 

A review, as far as possible, of the topics of the preceding 
grades, and, in addition thereto, the simple outlines of Physio- 
logy and Hygiene. 



WRITING. 

On Slates. — Continued as in the preceding grades. 

On JBaper, — Words containing difficult elementaiy forms ; 
also phrases and short sentences. Instruction and practice in 
the elementary forms, continued. 

DRAWING. 

Review of the work of preceding grades, to which add scrolls, 
and simple geometrical solids in outline, such as the cube and 
parallelepiped, in various positions ; also the cylinder, cone, pyra- 
mid, and prism. The drawings of simple objects, domestic 
utensils, etc., may also, occasionally, be copied from cards. 



BEADING. 177 



How TO Teach, 



SUBJECTS OF THE THIRD GRADK. 



LANGUAGE. 

Meadiiig, — In the preceding grades, due attention 
is required to be given to emphasis and modulation; 
but in this grade the exercises should take the special 
direction indicated by these departments of elocution, 
so as to lead to the higher stages of this art, required in 
the more advanced grades. It is not enough that the 
pupils should be accustomed to read with clear articu- 
lation and proper inflections of the voice ; they should 
be taught expressio'U — to comprehend the character of 
the piece read, to enter into its spirit, and, to some ex- 
tent, at least, communicate it justly and forcibly. 

Considerable attention should also be given to vocal 
culture. For this purpose exercises should be employed 
with the view to impart the physical as well as mental 
capabilities required for this purpose. The pupils should 
be taught the proper position of the body, and the right 
mode of using the lungs and the vocal organs so as to 
make their utterance effective. This kind of discipline 
has a most important bearing upon the general physical 
development of the pupils, as well as on the invigoration 
of the organs specially concerned in vocalization. 

For the attainment of the special objects of this 

grade, the elocutionary rules, principles, and exercises 

contained in the Keader, should be made available : a 
8* 



178 SOW TO TEACH 

portion of each reading-lesson being devoted to this 
kind of instruction and practice. 

It is essential that the pupils should be required to 
stand while engaged in these exercises — either the whole 
class, or the particular pupil called upon to read. The 
other pupils, in a proper manner and in the right spirit, 
may be permitted to criticise the performance of the one 
called upon to read, and to exemplify the criticism by 
reading the same passage. 

Lessons, especially such as involve a difficulty, should 
not be hurried over ; they should be read and re-read, 
until an approximation, at least, to correctness has 
been attained by one or more pupils. 

Concert reading and declamation may be resorted to 
occasionally, with very beneficial results. 

Spelling. — Oral spelling, except for the purpose of 
teaching syllabication^ should be discontinued. The 
proper division of words into syllables is an important 
matter, and should receive due attention. In this con- 
nection the correct use of the liyplien in compounds 
should be taught, and the pupils exercised therein. 

The ivritten exercises should be correctly performed, 
with care not only as to penmanship, but as to capitals, 
punctuation, etc. These exeixises should be carefully 
inspected, and after the errors have been pointed out, 
should be revised and corrected by the pupil himself The 
sentences used for dictation should contain a sufficient 
number of common test-words, iucluding proper names, 
both of persons and places, so as to impress the orthog- 
raphy of such terms firmly on the pupils^ minds. 

Definitions. — For suggestions, see the preceding 
'grade. 



GRAMMAR I79 

JEhiglisli Gra'ininajr. — Analysis, parsing ^ndi con- 
striLction are to be continued in this grade, the class of 
sentences employed being of a more diflicult character, 
but still carefully kept within the assigned limits of 
^^easy complex and compound sentences/^ 

By these are meant such as involve: 1. Complex sen- 
tences, containing simple adjunct clauses, or brief 
clauses used as subjects, objects, or attributes, — those 
containing long and involved or intricate phrases being 
reserved for the next grade; 2. Compound sentences, 
formed by the union of simple clauses, or of complex 
clauses, such as those above described. The analysis 
should be sufficiently minute, to keep before the pupil's 
mind the relations upon vrhich grammatical distinctions 
are based. The simplest phraseology should be used. 

The exercises in construction should be made to 
correspond with the advanced character of the analysis ; 
and the pupils, in the "short compositions^' required to 
be written, should, as far as possible, exemplify the in- 
struction in the other portions of the subject. They 
should be required to analyze and parse the defective 
sentences which occur in their own compositions, so as to 
discover the inaccuracies and to apply the necessary 
principles and rules for their correction. 

The exercises for the special purpose of accustoming 
the pupils to care and criticism in the use of language 
should be continued. 

Composition. — The compositions should, as far as 
possible, be impro77ipttc, and written under the immediate 
inspection of the teacher, so that the pupil may be made 
to depend upon himself in performing what is required. 
M-uch practice of this kind is needed before the formal 



180 ROW TO TEACH 

writing of compositions is assigned as a home tash To 
many pupils this very essential part of school education 
is made utterly repulsive by the impossible requirement 
that they should^ with scarcely any previous training, 
write out at their homes^ long compositions on difficult 
themes assigned by the teacher. 

The compositions proper for this grade should be 
hrief, and on simple suijeds, which should be either 
selected by the pupils themselves^ or, when prescribed 
by the teacher, should be of such a character as to in- 
terest the mind of a child. Those Avhich require the 
pupils to relate the incidents of their own experience — 
what they have seen, heard, or enjoyed, are chiefly to 
be preferred, since they are thus required to make use 
of their own language, while their attention is given 
rather to the thought than to the expression. And this 
is an important consideration; for exercises of this kind 
should not be designed to teach the use of language sim- 
ply, but language as the vehicle of thought. 



AEITHMETIO. 

Mental Arithmetic — For the purpose of review, 
brief examples in fractions, both common and decimal, 
should be employed, both as a test, and more thoroughly 
to fix in the pupil's mind a knowledge of the principles 
and applications of fractions as taught in the preceding 
grades. The improvement made by the pupils in ac- 
curacy and rapidity, as well as in the ready application 
of arithmetical principles to particular cases, involving 
an exercise of the judgment and reasoning powers, 
should be progressive from grade to grade, and there- 
fore should be carefully tested in the mental work. 



ARITHME2IG, 181 

The special proyince of this grade being Denominate 
Numlers, the exercises, both in mental and written 
arithmetic, should deal largely with the applications of 
fractions to that class of numbers, including Fed- 
eral money, and should, of course, combine practice in 
all the essential tables of weight, measure, etc. 

The teacher need not, perhaps should not, conform 
himself to the order or kind of examples presented by 
any particular text-book. If the questions given out to 
the pupils to be solved instanter are spontaneously con- 
structed by the teacher, they will be more appropriate 
to the special needs of the pupils, and the exercise will 
have far more spirit, and be of much greater value. It is 
among the dullest of all the occupations of the class- 
room to read from a book questions in mental arithme- 
tic, of little variety, hackneyed in form and character, 
and which the pupils have previously been required to 
con over. To expect an uninterested, drowsy class to 
perform any intellectual exercise, is absurd; but the 
absurdity is greater, perhaps, in mental arithmetic than 
in any other subject. For suggestions in relation to 
this point the teacher is referred to the statements made 
under the fifth grade. 

The review of the analysis previously taught should 
be systematic and thorough, but should not consume a 
large part of the time of the pupils. 

Written Arithmetic. — The arithmetic specially 
prescribed in this grade, both mental and written, is 
of a practical character, perhaps more generally so than 
in any other grade of the course. All that precedes 
has been, to a considerable extent, a preparation for the 
work of this grade, and will be found involved in it. 

The whole subject of compound denominate numbers 



182 ^OW TO TEACH 

is strictly utilitarian. Practical utility should, there- 
fore, be the controlling element in all the exercises em- 
ployed. The daily necessities of the house, the shop, the 
market, etc., indicate the general character of the selec- 
tions to be made. These will furnish at least as good 
mental discipline in calculation and analysis as those of 
a less severely practical character. 

It is usually the case, that pupils who have reached 
this grade can spend but little more time in school. In 
view of this fact it is important to attend first to the 
more practical, and therefore more essential, parts of the 
arithmetic of the grade. To this end, the tables, its in- 
dispensable basis, should be thoroughly reviewed, and not 
only memorized, but understood. Pupils should be 
trained to work with reasonable rapidity, and all long 
and complex examples, as well as those involving ob- 
solete weights, measures, or money, should be care- 
fully avoided. Eeduction should not be so long dwelt 
upon as to lead to the omission of important practical 
points in other rules. It is desirable that a record of 
the points covered by the class-work should be method- 
ically kept to be used as a basis of the necessary re- 
views. 

Syllabus. 

Heduction Descending. — Show why it is so called. The 
denominations should always be written with the exam^ 
Pupils should not be allowed to "add in'' by a separate line; 
it greatly increases the work, absorbs the time unprofitably, and 
indicates mental feebleness. The explanation or analysis should 
be given by processes which make the multiplier an ahstract 
number. The impossibility of multiplying by a concrete number 
should be carefully shown. 

As an illustration of the above, suppose the question to be, 



ABITHMETia 183 

" How many pints in 75 gallons, 3 quarts ? " There are at least 
two correct methods of analysis for this question. 

Analysis 1. — Since 4 quarts make 1 gallon there are 4 times as 

gals. qts. many quarts as there are gallons (75), which are 

75 3 300 quarts ; 300 quarts and 3 quarts are 303 

quarts ; and since 2 pints make 1 quart, there are 

303 qts. twice as many pints as there are quarts (303), 

—-7 , which are 606 pints. 

606 pts. 

In this analysis the work done on the slates is directly ex- 
plained, the multipliers 4 and 2 used in the slate-work and in the 
analysis being identical. 

Analysis 2. — Since in 1 gallon there are 4 quarts, in 75 gallons 
there are 75 times 4 quarts, which are 300 quarts ; 300 quarts and 
3 quarts are 303 quarts ; and since in 1 quart there are 2 pints, 
in 303 quarts there are 303 times 2 pints, which are 606 pints. 

In this analysis, which is concise, and perhaps more clear 
than the other, the w^ork done on the slate is indirectly ex- 
plained, the multipliers 75. and 303 not being those actually 
used. When this method is employed, an illustration of the 
following principle should be occasionally required : " The prod- 
uct of two or more abstract numbers is the same, whatever 
may be the order of the factors.*^ Also the modification of this 
principle, in the case where one of the numbers, as in the given 
instance, is concrete. 

The following errors are frequently heard and should be 
avoided : '' I multiply 75 gallons by 4 quarts, etc." Four quarts 
times 75 gallons is, of course, absurd. 

. I multiply 75 . gallons by 4, etc. Four times 75 gallons is of 
course 300 gallons^ not 300 quarts. 

It will be seen that the above analyses and that required for 
Reduction Ascending are identical with those already given in 
the preceding grades. The '* adding in" is the same as in the 
reduction of mixed numbers. 

JReduction Ascending,— Tim is best taught and under- 
stood in immediate connection with Reduction Descending, at 
first by reviewing the same example. Long division by divisors 
less than 13 should not be allowed, nor if cutting off O's will 
change to short division. 



184 S:OW TO TEACH 

Explanation may be by any process which will clearly ac- 
count for the denominations of the successive quotients and re- 
mainders. 

Weights, — Teach briefly by examples the relations of Avoirdu- 
pois and Troy weights, and the essential identity of Troy and 
Apothecaries' weights. Let most of the examples in Reduction 
be in the first of the three. They should be few and very short 
in the last. 

Remember that the quarter of a hundredweight is seldom 
used now, excepting in text-books — the Avoirdupois dram no- 
where else. 

In addition and subtraction, give only Avoirdupois weight. 
Remember that in things sold by the ton, the ounce is not tal^en 
into account. Review the principle of carrying, if that plan 
is used ; of its better substitute, if not. A short question in Troy 
weight may be written upon the board or read from the text- 
book if pupils have one. Then require them to state succinctly 
what process will be required in working it, omitting detailed 
analysis. 

Note.— To avoid repetition, it may here be stated, that the plan just men- 
tioned may be taken in multiplication and division as well as in reduction, 
addition, and subtraction, with those portions of the weights, measures, 
etc., practice in which is of less general utiUty. Many practical examples in 
multiplication and division will arise under Avoirdupois weight, such as 
finding values at so much a pound, hundredweight or ton, or vice versa. Such 
examples may involve preliminary addition or subtraction, or both 

Linear Measure. — Reduction. — Employ the denominations 
most in use — the inch, the foot, the yard, the rod, and the mile 
— very rarely, if ever, all in the same example. Omit cloth 
measure, or if briefly referred to, use only is, ^s, iths and fe^hs. 
Give a very few examples to show the use of the chain and its 
subdivisions. Measuring-tapes usually have feet on one side and 
chains and links on the other. One may be employed to advan- 
tage in the class-room. To convert feet or yards into miles, and 
mce wrsa^ use only 5,280 and 1,760; for instance, so many miles 
of railroad track having so many lbs. of iron to the yard, at so 
much a ton, etc., etc. Omit addition and subtraction, multipli- 
cation and division. 

Surface Measure. — {Of very great practical importance.) — Treat 
briefly in reduction. When 30i is used as a divisor let it be in 
very short examples. Give examples in addition and subtrac- 



ARITHMETIC. 185 

tion. In multiplication and division give examples in finding 
areas of rectangular figures, in feet, in yards, etc. Give the feet, 

or the chains, on the sides of rectangles, to find acres and vakie ; 
acres and hundredths the most usual form. Omit roods. Sim- 
ple questions may be given occasionally, involving cost, in esti- 
mating for plastering, bricks, carpets, di'ess-linings, etc. ; also 
veiy simple questions in finding the area, circumference, or di- 
ameter of a circle when square root is not inwlwd, using ft or 
3.1416 for ratio. 

Solid Measure. — Employ only the inch, the foot, the yard, and 
the cord ; use the last but little. See that pupils understand the 
mutual relations of linear, sm'face, and solid measures, and that 
they are not convertible, the units being of totally different na- 
tures. Reduction — a few simple questions. Omit addition and 
subtraction. Give examples in finding cubic inches, feet, or 
yards, in boxes, bins, cellars, cylindrical cisterns, etc., etc. 
Some knowledge of hoard measure, giving very simple practical 
examples involving cost. 

Dry and Liquid Measures. — Use no obsolete denominations. 
Omit beer measm'e. Eemember that the barrel and the hogs- 
head are not often measures in commerce. Sirpple examples in 
reduction. Omit addition and subtraction. Give the simplest 
possible examples, in connection with solid measure, in finding 
bushels or gallons in bins, vats, cisterns, etc., using 231 and 
2150 cubic inches, and omitting fractions. jSTo other multiplica- 
tion or division should be required. 

Circular Measure. — Treat briefly ; explain the terms and their 
use ; omit signs. Reduction — Short examples of two or three 
terms. Addition and Subtraction— Questions in difference of 
latitude and longitude. Geographical and statute miles on the 
meridian, on the equator, on parallels of 60^ 

Time. — (In part veiy important.) Treat reductions very 
briefly. Do not involve more than two or three denominations 
in one example. Leap-year. Addition and subtraction. Dif- 
ference of dates — by days, and by years, months and days. Re- 
lations of difference of longitudes to time. Explanations and 
examples. Conversion of longitude into time and mce 'versa. 

Miscellaneous. — Practical examples in values, involving dozen, 
gross, quire, ream, quintal, barrels of flour, fish, etc., making 
out simple bills, receipts, etc. 



186 HOW TO TEACH 

Money. — Reduction and other simple exercises in Federal 
money are always in order from the Fifth Grade. Give but 
few examples in each rule in sterling money. Reduction of 
sterling to Federal and vice mrsa^ omitting, of course, all refer- 
ence to the percentage of exchange. 

Pupils should know something of the money of Canada — 
identical with our own — the value of the franc, and the dollar 
of the Zollverein. 

Fractional Compound Numbers. — The consideration of this sub- 
ject has been deferred to avoid complicating it with simpler and 
more important matters. Reject all exaglples in addition, sub- 
traction, multiplication, and division. In reduction there are 
hut twQ cases J and the second of these is simply the cod verse of 
the first. Each divides into two varieties, in one of which the 
fraction is common and in the other decimal, but the principle 
applied in working is the same. 

Be careful to select only those denominate numbers in which 
such fractional quantities are likely to need consideration, chiefly 
sterling money. 

( A. f f of a bushel to pecks, quarts, etc. 
Examples : Case 1st. -j B, .673 of a £, how many shillings, pence, 
( etc., or dollars and cents. 

A. 7ft. 95 in., what common fraction of a 
cubic yard ? 

B. 15 cwt. 38 lbs. are what decimal frac- 
tion of a ton ? 

£8 14s. d^d are how many dollars and 
cents (at $4.8661) ? 



Case 2d.^ 



GEOGRAPHY. 

SOUTH AMEEICA. 

Ziocal Geography* — Begin with the continent of 
South America, as a whole, its boundaries, the names 
and relative positions, or boundaries, of its political 
divisions — a few of the chief capes and islands, the posi- 
tion and direction of the great plateaux and mountain 
ranges [use chalk sections roughly drawn on blackboard] 
— five or six of the most famous volcanoes. In the 



GEOGRAPHY. 187 

drainage, only two or three lakes, the courses of the 
Orinoco, the Amazon, the San Francisco, and the Pa- 
rana described, and their great branches named and 
pointed out as systems, but not described. 

The local geography of the several countries taken 
separately should be yery brief, and should include a 
review of the matter previously considered in the study 
of the continent — that is, the relative positions or 
boundaries, the positions of the mountains and pla- 
teaux, the principal rivers, etc., etc., together with the 
capitals of the several countries, and about twenty-five 
of the other principal interior cities and seaports of the 
continent. 

Descriptive Geography. — It will also be found 
most expeditious and effective to teach the descriptive 
geography of the continent first as a whole. From 
this, that of the several countries may be very easily 
deduced and distinctly remembered. It should include 
the surface of the country as mountain, plateau, or 
plain ; the zones ; the climate as modified by latitude, 
elevation, and the prevalent winds ; the leading char- 
acteristics of the great plains and plateaux ; a brief no- 
tice of volcanoes and eartliquahes ; a few of the princi- 
pal />Za7i^5 and animals; the three r<2<?e^, their distribu- 
tion, and their principal occupations, and the influence 
of the physical geography thereon ; the European la7i- 
guages spoken; the chi^f productions 'diidi exports, vege- 
table, animal, and mineral, and the forms of govern- 
ment. 

EUROPE. 

Local Geography. — The geography of Europe 
should be so taught as to avoid the presentation of a 



188 HOW TO TEACH 

large amount of minute detail. In local geography the 
boundaries of the continent, the names and relative po- 
sitions or boundaries of its states; the position of its 
principal peninsulas, capes, gulfs, bays, seas, and straits; 
its chief highlands and lowlands ; from twelve to fifteen 
principal mountain systems, the famous volcanoes, the 
great islands and groups of islands, seven or eight im- 
portant lakes, including two or three in Switzerland ; 
from twenty to twenty-five of the important rivers, spe- 
cifying those w^hich are important as commercial water- 
ways ; the names and positions of the capitals of the 
several countries, and from fifty to seventy of the other 
important cities. 

Descriptive Geograx>hy. — The descriptive ge- 
ography to be on the same plan as for North and South 
America. It should include the general surface, climate, 
and productions, the people and their industries, to- 
gether with their relations of blood, language, com- 
merce, etc., with the people of the TJnited States. In 
reviewing the chief cities, state any important or inter- 
esting facts in relation to each. 

Mevietv. — The topics of the preceding grades should 
now be reviewed in outline. 

ThiS'lmportant requirement may best be met by mak- 
ing the exercise a comparative one. It should not be a 
home-lesson, but a vigorous class-room exercise, dis- 
carding for the time the text-book, and using the out- 
line maps, the pointer, and the globe. For instance, a 
rapid pointing out and naming of all the countries of 
America and Europe, and their capitals, might consti- 
tute one lesson; all the mountain systems, plateaux, 
plains, and volcanoes, another; the climate and produc- 
tions, a third ; and so on. 



UISTORY. 189 

HISTORY OF THE UNITED STATES. 

General Suggestions. — The leading purpose oi 
this study is that the pupil may understand the origin, 
character, and condition of the nation of which he is a 
part, and that he may be fitted for an intelligent exercise 
of his duties and responsibilities as a citizen. 

It is obviously impossible to treat so comprehensive a 
subject exhaustively. The immaturity of the pupil's 
mind and the pressure of other studies alike forbid. 
Yet the leading facts and principles may be readily 
comprehended and remembered, and the outline which 
he is to retain be made from the first coherent and defi- 
nite. To this end a simple preliminary outline shetcli 
should be carefully fixed in the minds of the pupils of 
this grade, and frequently reverted to in the reviews of 
all the grades in which the subject is taught. The ge- 
ography already learned will greatly simplify the process. 
This outline can be given most expeditiously and efii- 
ciently by means of oral instruction and the use of the 
map. It should be very brief, and, if it be thought ex- 
pedient, should be reduced to writing by the pupil for 
reference. All detail should be reserved for the study 
of the text-book. 

The following sketch is presented only as illustrative 
of this suggestion. Its modification by re-arrangement 
or otherwise, or the substitution of another in its place, 
may be found desirable. 

Outline Sketch. 

* 

1st. The people of the United States are of European descent, 
excepting the negroes. 

2d. Less than 400 years ago our ancestors knew nothing of 
the existence of this continent. ' 



190 BOW TO TEACH 

8d. Spain, guided by Italian genius, led -the way to its discov- 
ery, exploration, and colonization. 

4tli. The first permanent English settlement within our limits 
was not eflTected until more than a century after the voyage of 
Columbus. In the interval, Spain and Portugal had possessed 
themselves of the shores and islands of the Mexican Gulf and of 
nearly all South America. 

5th. For a century and a half the English colonies were con- 
fined to a narrow strip east of the Alleghanies. 

6th. Spanish slaver}^ exterminated the Indians of the West 
Indies. This led directly to the opening of the African slave 
trade, and indirectly to the introduction of slaves into our own 
country. 

7th. The colonies had wars with the Indians m whose coun- 
try they had settled, and with the neighboring French colonies. 
The French were subjugated and their territories occupied. 

8th. Less than a century ago all European settlements were 
still dependent colonies. 

9th. The necessities of distant colonial settlements had de- 
veloped in the English colonies a spirit of self-reliance and .po- 
litical freedom, and a system of local and elective self-govern- 
ment. 

10th. The expenses of the French wars left a heavy debt and 
led to unusual taxation. A tyrannical system of taxation led to 
the War of Independence, which fixed the national boundary 
at the Mississippi. The colonies had become States. 

11th. The present form of government (the Constitution) was 
established soon after the close of the war, about eighty-three 
years ago. * . 

12th. The number of States has been greatly increased by im- 
migration and emigration. The population and wealth have 
increased many fold. 

13th. By purchase and otherwise the national territory has 
been expanded to the Gulf of Mexico and to the Pacific and 
Arctic oceans. 

14th. 'Since the War of Independence there have been three 
important wars : 1. A war with England vn defense of naturalized 
citizens and in vindication of the rights of neutrals ; 2. A war 
with M§xicOj resultiug from our annexation of Texas; 3. A great 



HISTOBT. 191 

civil waVy arising in part from questions originating in our colo- 
nial history and in part from more recent causes. 

Lessons and Recitations. — Lessons m ni^^ory should 
be assigned by topics and not by pages. 

All yerbatim recitations of sentences ana paragraphs 
should be strictly forbidden^ and the pupils should be 
required to state the facts in their own language. 

Only such dates should be committed to memory as 
are indispensable as landmarks in • history. The se- 
quence of events, rather than the precise date of each, 
is what is chiefly necessary. 

Maps, especially those of the text-books, snould be 
used whenever the subject may require it. 

Historic episodes, however interesting, should not re- 
ceive the careful study given to the essential narrative. 
The stories of Juan Ponce de Leon, the Conquest of 
Mexico, De Soto's Expedition, John Smith, Pocahontas, 
the Salem Witchcraft, etc., should indeed be carefully 
read, and, as far as may be necessary, explained; but, 
unless great care be taken by the teacher, the pupils will 
be apt to conceive that these are the most important 
portions of the history. 

Important incidental allusions to European history, 
such as the rise of the English Puritans, the expulsion 
of the Stuarts, the French Eevolution, etc., should be 
carefully but briefly explained. Great caution should 
be exercised throughout these lessons to state the facts 
in such a manner as not to wound the religious or 
political sensibilities of any. 

JRevietvs. — Eeviews of the portion already taught, 
with frequent references to the preliminary sketch, are 
of the highest importance. These reviews should take 
three distinct forms: the Chronological, the method 



192 ^OTF TO TEACH 

usually followed in the text-book; the Biograpliicaly 
requiring the pupil to state all that has been learned in 
regard to particular individuals; and the GeograjjMcal^ 
requiring a statement of all important facts relating to 
the history of a locality. Many of the topics treated 
by the second and third of these methods necessarily be- 
come cumulative. For instance, the facts relating 
directly to George Washington will be gathered from 
at least three distinct and important periods in our his- 
tory. A connectec^ statement of the important events 
that have taken place in Philadelphia, or in the valleys of 
the Hudson and of Lake Champlain, or in the State of 
Virginia, will necessarily cover a large part of the gen- 
eral subject in the higher grades. Such statements 
must, of course, be brief, and will often be a mere chro- 
nological table. 

Many of these reviews and certain parts of the regu- 
lar recitations may be made spirited general exercises 
for the whole class by the use of the slate or of paper. 
The writing of the few essential dates, the sequence of 
important events, the names of important individuals, 
etc., are instances. The narrative reviews will neces- 
sarily be, for the most part, oral. 

It will be observed that the system of reviews above 
suggested must, if faithfully carried out, result in a 
thorough unifying of the general subject in the mind 
of the pupil. 

Suggestions for the Third Grade. — The 

essential points requiring careful study and frequent 
review in the history assigned to the Third Grade are 
given below. Other interesting facts usually stated in 
text-books should be carefully read, but should receive 
a less proportionate share of attention. In no other 
grade is a frequent reference to the maps so important. 



HISTOBT. 193 

Syllabus of Topics. 

The voyage of Columbus ; the naming of America ; the occu- 
pation of the West India Islands and all the neighboring por- 
tions of the continent by the Spaniards ; their enslavement of 
the Indians and its results (the last very briefly). 

The discovery, exploration, and occupation of the St. Lawrence 
and Nova Scotia by the French. 

Virginia. — Th settlement of Jamestown and the events 
directly leading to it. The cultivation of tobacco ; the intro- 
duction of slavery ; the navigation acts and Bacon's rebellion. 

Maryland. — The Calverts ; religious freedom ; Clayborne. 

New England. — The Plymouth Company and the settlements 
under their patent. The Puritans ; their previous history and 
why called Pilgrims. The settlement of Plymouth ; of Boston ; 
of Dover ; the Massachusetts Bay Colony. The settlement of 
Connecticut; of Rhode Island; provisions for religious freedom. 
The Union; Indian Wars {i^ead only, and do not commit the 
details to memory). Andros ; King William's War, its causes 
and results. The Salem Witchcraft (read). Queen Anne's War, 
its causes and results. King George's War, its causes and 
results. 

New NetJierlands. — Henry Hudson ; the settlement on the Del- 
aware ; at Fort Orange ; at Manhattan Island ; the Dutch Gov- 
ernors ; Kieft's conduct ; Stuyvesant. 

New York. — Changes of name ; reconquest by the Dutch and 
final restoration to England. Andros ; the extent of his rule. 
Dongan; Leisler; the burning of Schenectady; the Negro plot. 

New Jersey. — Its name ; its division ; union with New York ; 
final separation. 

Delaware. — Its settlement by Swedes ; its conquest by Stuy- 
vesant. 

Pennsylvania, — William Penn; his grant; his objects. The 
settlement of Philadelphia; the relations of Pennsylvania to 
Delaware. 

NortJi Carolina. — The grant of Charles II. ; its geographical 
limits ; John Locke. 

South Carolina. — Charleston settled ; Carolina divided into 
two separate governments in 1729. 

Georgia. — Savannah settled ; character and purposes of Ogle- 
thorpe. 

9 



194 ROW TO TEACH 

The general condition of the English colonies in 1752. Their 
population ; their national derivation ; their industries, social 
condition, planters, patrons, and proprietors ; the causes which 
were developing a love of liberty. 

Eeview chronologically under heads of the following sovereigns 
of England : Elizabeth ; James I. ; Charles I.; Cromwell ; Charles 
II.; James 11. ; William and Mary; Anne ; George I.; George II.; 
also, 5^^^rap/^^ca%, referring to Columbus, De Soto, Cortez, Car- 
tier, Ealeigh, etc., etc. 

The French and Indian TFar.— This should be taught in out- 
line, the principal points being :— The gradual extension of the 
English and French settlements leading to conflicting claims ; 
the explorations and posts of the French in the valleys of the 
Mississippi, the St. Lawrence, and the Lakes ; Marquette and 
La Salle ; the debatable land on the upper Ohio ; relatively 
small population of Canada ; the building of Fort Du Quesne, 
1754; Colonial Congress at Albany, 1754; Braddock's and 
Johnson's Expeditions, and their results, 1755 ; Monckton's 
Expedition in 1755 ; cruel expulsion of the Acadians ; capture of 
Oswego, 1756 ; Fort William Henry, 1757 ; siege and capture of 
Louisburg, 1758 ; repulse at Ticonderoga, 1758; concentration 
of French forces at Quebec, by abandoning nearly all other 
posts ; battle of Quebec, 1759 ; results ; Treaty of Paris, 1763 ; its 
conditions. 

In teaching the French and Indian War let the ten dates 
marked be studied by the years only. Read, but do not memor- 
ize, the details of military movements and events ; fix the se- 
quence of events ; use the map. 

In the biographical review, let the pupil tell very briefly of 
Washington, Braddock, Johnson, Monckton, Amherst, Aber- 
crombie, Howe, Wolfe, Dieskau, and Montcalm. 

ELEMENTARY SCIENCE. 
(For Oral Instruction.) 

PHYSIOLOGY AND HYGIE:^E. 

The chief purpose of this study as a branch of Com- 
mon School instruction is, to give useful practical 
knowledge of the laws of health. As the subject can 



ELEMENTARY SCIENCE, 195 

receive, at most, but a small part of the time assigned to 
a single grade, it is the more important that only those 
parts of the study should be considered that are essen- 
tial to the main purpose. Anatomy, which occupies so 
much space in many text-books, should not take up the 
time of the pupil, excepting so far as it may be absolutely 
necessary in order to teach the physiology and hy- 
giene. It is a matter of little consequence to the pupil 
to know exactly the number of bones, or of pairs of mus- 
cles in his body, or to repeat their scientific names. 
Only those terms and facts should be introduced that 
are actually necessary in order to deal intelligently 
with the main subject. Oral descriptmi of structure 
or function should take the j)lace of definitions. 

The appliances necessary for teaching this branch are, 
the blackboard and charts. The teacher should care- 
fully consider, at every step, to what extent the subject 
can be treated objectively. This can, in part, be done by 
drawing the pupiFs attention to his own body, as in 
the case of the pulse, the veins, arteries, respiration, etc. 
For several very important parts of the subject, there is 
no better apparatus than that which can be procured 
without expense at any butcher's stall, such as the lungs 
and windpipe of a sheep ; the diaphragm, the heart and 
part of the great tubes leading to and from it ; the brain 
and the bony cavity which contains it ; the eye ; por- 
tions of the spinal cord and nerves ; small glands ; and 
portions of limbs, showing the relations of muscles, ten- 
dons, ligaments, and joints. None of these need present 
anything offensive or disgusting. Add to these a small 
knife, and reasonable preparation on the part of the 
teacher, and the instruction given will be both interest- 
ing and profitable. Where it would not be expedient to 
resort to this means of illustration, preparations (simi- 



196 HOW TO TEACH 

lar to those manufactured by Auzout) could be used, if 
procurable, and in their absence, diagrams and charts. 
A syllahits of leading points is subjoined. It should 
not be expected that all these can be taught in one 
class, though all are important, nor that any point 
should be treated exhaustively. 

Syllabus of Topics. 

• The pupil should be led to look upon the body as a complex 
apparatus for the use of his mind. To know that it consists pri- 
marily of — 

Firsty a bony frame-work (the skeleton) ; second, a motor ap- 
paratus attached to the frame (the muscular system) ; third, a 
directing apparatus by which the mind controls the body (the 
brain, the nervous system, and the sensory organs) ; fourth, a 
general envelope protecting all the preceding, as well as serving 
other purposes (the skin). 

He should then be led to see that every motion of the body or 
of its minutest part, however slight, and whetlier voluntary or in- 
voluntary, requires the destruction of a minute part of the organ- 
ism and the removal of the destroyed part from the S3^stem ; 
that this constant destruction and removal make necessary a cor- 
responding reconstruction and renewal, by means of new mate- 
rial ; and that for these purposes there are provided, fifth, a cir- 
culatory apparatus (the blood-vessels), to carry away old material 
and to distribute the new ; sixth, an aerating apparatus (the res- 
piratory system), to purify, warm, and enliven the circulating 
fluid ; seventh, a system of drainage (the skin and the kidneys), 
to take from the blood a large part of the worn-out material ; 
and eighth, an apparatus to prepare and supply the new ma- 
terial (the digestive and assimilative organs). 

Under each of these heads a few points are noted : 

1. The bones, — their composition and various uses ; joints and 
their lubrication ; important peculiarities of the spinal column ; 
cautions as to injuring the large bones of an infant ; the repair 
of broken bones, how effected. 

2. The muscles and tendons, — their uses ; their arrangement in 



ELEMENTARY SCIENCE. 197 

pairs, and why ; how attached ; how able to contract ; effects of 
exercise] use of calisthenics. 

3. The nervous system; — the means of becoming conscious of the 
external world; the spinal cord; its importance and protection; 
its ramifications; effects of severing or injuring the spinal cord; 
care of infants iu this respect. The sympathetic system ; the 
nerves as telegraph wires; the brain and its principal functions; 
uses of sleep ; late hours, stimulants, etc. 

The organs of the special senses, — touch, papillae ; taste ; smell ; 
the ear, its mechanism, hearing ; the eye, its mechanism, sight ; 
abuse of the eyes ; myopy, its causes and prevention. 

4. The skin^ — its structure and uses ; the perspiratory glands 
and tubes ; uses of perspiration ; importance of bathing ; the 
proper time for bathing ; proper clothing ; sympathy of the skin 
with the lungs, with the digestive organs ; caution against the 
exposure of the limbs, arms, or chests of little children ; the skin 
as an absorbent ; danger of cosmetics and hair-dyes ; treatment 
of burns and scalds, etc. 

5. The circulatoi^y system, — the general relations of the heart, 
arteries, veins, and capillaries ; the valves ; the pulse ; its rate ; the 
rapidity of circulation. Effects of fresh air and exercise on the cir- 
culation ; limits of exercise ; dangers of excessive rope-jumping, 
etc. Effects of sleep on the circulation ; effects of tight gar- 
ments ; of insufficient or improper food ; wounds ; how to know 
when an artery is wounded, and what to do. 

6. The respiratory s?/s^m.— (Practically the most important part 
of hygienic knowledge). The apparatus ; how protected ; ar- 
rangement of the ribs for flexibility, and for the expansion of the 
lungs ; the muscles of the chest and the diaphragm ; importance 
of the diaphragm; (show its positions at the beginning and at 
the end of an inspiration ;) the trachea ; the vocal chords ; 
structure of the lungs ; its air cells, and their membrane ; exos- 
mosis dnd endosmosis as concerned in respiration ; intimate re- 
lations of the capillaries and air vessels ; frequent full inspira- 
tions a means of increasing the capacity of the lungs ; perni- 
cious effects of tight lacing on the capacity and action of the 
lungs. The air, — its composition ; relations of oxygen to the 
carbon and the hydrogen introduced with the food ; products of 
respiration all invisible excepting watery vapor ; the poisonous 
nature of carbonic acid ; danger from it in wells, and in vats ; 



198 b:ow to teach. 

the effects of smaller quantities ; the other substances thrown off 
by the lungs and the skin ; the ventilation of class-rooms 
and of sleeping-rooms ; effects of foul air from cellars, sewers, 
sinks, water-pipes, garbage, gas-lights, stoves, etc. ; simple and 
cheap disinfectants ; chloride of lime ; chlorine ; sulphate of 
iron ; carbolic acid, etc. Respiration as affected by position, in 
standing, or in sitting, and especially in sitting to write or to 
draw. 

7. The digestive apparatus, — the teeth, their uses, sti'ucture, and 
hygiene ; a brief notice of the salivary glands, their position and 
uses ; of the gullet ; of the structure and function of the stomach ; 
a brief notice of the duodenum, the intestines, and the lacteals ; 
the importance and functions of the liver ; the thoracic duct as 
the link between the digestive and the circulatory systems. Dys- 
pepsia, its preventable causes and terrible consequences ; common 
errors to be avoided in the preparation of food ; common poisons 
and their antidotes. 



SEOOI^D GEADE. 

OUTLIKE COUKSE. 
Time allowed^ about ten months. 



LANGUAGE. 

Heading.— Of the grade of a Fifth Reader, with instruction 
and exercises in elocutionary principles, and in vocal culture, as 
in the preceding grade. 

Spelling. —QontimxQdi as in the preceding grade. 

Definitions.— A&m the preceding grade, with word analysis, 
or etymology. 

English 6rr•all^iW.ctr.— Analysis, parsing, and construction 
continued ; also the correction of false syntax. 

Composition. — Continued. 

ARITHMETIC. 

Mentat, and Written. — Commercial rules, through per- 
centage, including profit and loss, commission, insurance, stocks, 
interest, discount, etc. ; with carefully graded exercises in analy- 
sis and calculation. 

The problems, to teach and illustrate the methods of compu- 
tation employed in ordinary business transactions. 

GEOGRAPHY AND HISTORY, 

Geography. — Of Asia, Africa, and Oceanica, both local and 
descriptive ; an outline review of the topics of .he preceding 
grades. 



200 S:OW TO TEACH 



History. — Of the United States, from 1763 to the present 
time, including the outlines of the Revolutionary War, the forma- 
tion of the Union, the chief events of the national history, includ- 
ing also a hrief outline of the great Civil War of 1861-5, and ita 
results. 



ELEMENTAEY SCIENCE. 

BY ORAL INSTRUCTION OR WITH A SIMPLE TEXT-BOOK. 

Natural Philosophy. — The outlines of mechanics, hydro- 
statics, and pneumatics. 

Astronomy. — ^Elementary astronomy, to include an explana- 
tion of the ordinary phenomena, and a brief account of the bodies 
constituting the Solar System. 

WRITING AND DRAWING, 

^Penmanship, — Instruction and exercises of a similar char- 
acter to those of the preceding grade, but more advanced. 

J)ratt?ingr.— Continued practice in the work prescribed for the 
preceding grades, to which should be added the sphere, the ob- 
late and oblong spheroids, the hemisphere, with first lessons in 
shading ; also the drawing of rectangular solids from blocks in 
various positions, with a few simple directions as to perspective. 



BEADING. 201 



How TO Teach 

SUBJECTS OF THE SECOND GRADE, 



LANGUAGE. 

Meadinffo — In this grade, the simple principles of 
elocution, taught in the preceding grades, should be 
carefully reviewed, and exercises to cultivate the voice, 
and confirm habits of distinct articulation should be 
continued to some extent. The rationale of good read- 
ing should, as occasion offers, be more fully explained, 
particularly as regards emphasis and modulation. Emo- 
tional reading should receive a fair share of attention. 
In classes or schools for males, exercises in declamation 
and recitation will be useful as an auxiliary. 

The pieces read, being of a higher order of style and 
subject, should receive a more careful analysis on the 
part of the teacher, so as, by interrogation, to lead the 
minds of the pupils to a proper understanding of their 
subject-matter, and enable them to obtain all the i7ifor' 
mation and culture of mind which they may be made 
the vehicle of imparting. Much time is apt to be mis- 
spent in this grade by simply permitting the pupils 
to read mechanically and listlessly pieces of difficult 
prose and poetry, which by earnest teaching might be 
made to fix in the minds, and often in the hearts, of the 
pupils so much that is valuable. Few tests of the ear- 
nestness and skill of a teacher are so thorough as the 
teaching of reading in this grade and the next. The 



303 -EIOW TO TEACH 

subject, the style, the difficult or unusual words, the al- 
lusions, the course of reasoning, mode of treatment, 
etc., may all be made the basis of useful investigation 
by the pupil or of comment by the teacher. 

The pieces read should comprehend a sufficient vari- 
ety, both as to style and subject, toaflFord scope for what 
is above suggested. They should include didactic, narra- 
tive, argumentative and oratorical selections ; extracts 
from distinguished writers in history, biography, popular 
science, etc., as well as the various departments of poe- 
try ; an important object of the instruction being to give 
a taste for reading more fully the works or compositions 
from which the extracts are made. Some account of the 
authors should be given in connection with the lessons. 

Definitions and Word Analysis. — The pre- 
fixes and suffices learned in the preceding grades should 
be reviewed by means of appropriate exercises involv- 
ing the application of easy roots, Eor this purpose such 
words as the following may be used !.— Drunkard?, 
Thisilldomy Dep^fA, ^Sduct, Yersio?i, LocaZ, — involving 
English, or Anglo-Saxon, and Latin affixes only. 

Next, the exercises should involve the use of easy 
Latin roots, such words as the following being used : 
Avert, Advert, Convert, Fervert, etc. — verse, version, 
diverse, etc. The application of various affixes, so as to 
form several words from the same root, will serve to im- 
press the meaning of the root, in its various forms, on 
the mind of the pupil, as well as to review the affixes. 
Latin words need not be taught. 

After a few exercises of this kind, words containing 
miscellaneous roots maybe used; as, Pre^/ic^, ^nhmit, 
'Reject, Invade, etc. ; then words containing prefixes and 
suffixes, as, Submission, Ohjection, Gonfiueni, Vxocednve, 



DEFINITIONS AND WOBD ANALYSIS, 203 

etc. ; care being taken at first to select such words as 
are regularly formed, and the literal signification of 
which exactly or nearly agrees with the actual meaning 
as used. 

The folloAving form of analysis is suggested: Aiducf, 
— formed from the root duct which means to lead, and 
the prefix ab, which means away. Hence, ahduct 
means to lead away. Actual meaning, to talce aiuay hy 
stealth ; as, " They tried to abduct the child from his 
parents.^^ 

In -this form of analysis, the root and its meaning are 
first stated; next, the suffix ; then, t\ie prefix, and then 
the literal meaning of the word, to be followed in all 
cases by the actual meaning, which is to be exemplified 
in a sentence. 

After the pupil is sufficiently initiated in the method 
so as to analyze words with some degree of facility, the 
principal Latin roots should be taken up and taught 
exhaustively, alphabetically, or in the order of their 
difficulty. These should be followed by a few of the 
Greek roots, suffixes and prefixes, to be followed by the 
French or other foreign roots. The Anglo-Saxon or 
English roots should, if taught at all, follow these. 
All beyond the Latin roots, and if necessary some of 
these, may be reserved for the First Grade, 

Exercises in the fo7'7nat ion of tuords from given roots 
should form a prominent part of the exercises used to 
familiarize the pupils with the meaning of the roots, as 
well as the meaning of words derived from them. For 
the purpose of this instruction the English form of the 
root is all that needs to be taught. In this way the 
subject will be freed from much complexity. Thus, 
after analyzing the word dentist, the pupil gives, as far 
as he can recall to mind, the words derived from the 



204 ^OW TO TEACH 

root dent j as denfsl, dentsite^ dentoid, dentition^ denti- 
frice, dentiiovm, mdent, etc. Words such as dentistry 
are to be considered as of secondary formation, and to 
be analyzed by considering dentist the primitiye. In 
this way the analysis of a very large class of words will 
be greatly simplified. 

The analysis of words is, of course, etymological ; but 
it is rather introductory to the study of etymology 
than, properly considered, a part of that study. The 
science which treats more directly and specially of the 
origin and relation of verbal forms, their primitive 
meaning, their combinations, and the varied significa- 
tions with which their derivatives have been used from 
time to time, is scarcely appropriate at this stage of the 
pupil's progress. The instruction derived from such 
exercises as are above indicated is exceedingly valuable 
for its practical usefulness ; but such facts as that half 
is the Anglo-Saxon Tiealfy Tiome the Anglo-Saxon lidmj 
and the German heim, etc., etc., are interesting and 
useful for a very different purpose, and should occupy 
a more advanced place in an educational scheme. 

English Grammar. — In this grade, the pupils 
should be exercised in the analysis smd parsing of sen- 
tences of a higher grade of difficulty ; but those of anom- 
alous or peculiar construction should be avoided. The 
analysis, except for review, should be only in outline, 
so as to show the ^^ general structure of the sentence,'^ 
and enable the pupil to see clearly the relation of the 
clauses or members. This is essential to a correct and 
definite understanding of the meaning of the sentence, 
as well as for the application of rules having reference 
to the construction of sentences. Some knowledge of 
punctuation should be imparted in this connection. 



GRAMMAR. 205 

The following sentence analyzed will illustrate the 
requirements of this grade in this respect : 

''Pay the debts which thou oiuest ; for he who gave 
thee credit relied upon thy honor, and to withhold from 
hi7n his due is ioth mean and unjust/^ 

Analysis. — This sentence consists of two members: 
1. ''Pay the debts/' etc., to " ozuest ;^' 2. "He tvho gave 
thee,^' etc., to " unjust/^ These members are connected 
by "for:' 

The first member contains the clause "which thou 
02vest/' used as an adjunct of " debts.'' 

The second member consists of the two clauses : "He 
who gave thee/' etc., to "honor/' and "To loithhold/' 
etc., to " unjust/' 

This should be followed by the 'parsing of the most 
important words, which will show whether a more mi- 
nute analysis of the sentence should be required of the 
pupil or not. 

As far as may be necessary, the. structure of the sen- 
tence, discovered by analysis, should be made the subject 
of rhetorical criticism, with reference to its clearness in 
expressing the meaning intended to be conveyed, \\.^ pro- 
priety, unity, harmony, etc. The thought itself may be, 
to some extent, analyzed, and subjected to critical remark. 

The "parsing, as an application of the rules and prin- 
ciples peculiar to our own language, should also, as 
far as possible, be so conducted as to have a critical end 
in view. This will greatly improve the pupils in their 
use of language, by rendering them more alert in dis- 
covering inaccuracies, as well as by impressing more 
deeply upon their minds a knowledge of the rules by 
which they should be guided in expression. 

Exercises in the correction of false syntax should be 
abundantly used in this grade. 



206 b:ow to teach 

Composition. — The construction of sentences 
should assume the character of extended composition, 
the themes being selected by the pupils themselves or 
assigned by the teacher. Of course, care should be 
taken that the themes are of a simple character — ap- 
propriate to the mind of a child, and calculated to 
awaken thought, not to repress it, as is too often the 
case when difficult subjects, of an abstract or too 
comprehensive character, are chosen for the exercise. 

AEITKMETIC. 

The commercial arithmetic of this grade differs from 
that taught in the preceding grades, chiefly in the in- 
troduction of the various forms of percentage. The 
divisions of percentage should be presented in the fol- 
lowing order : First, simple percentage, in four cases — 
one fundamental and three derived; second, the appli- 
cations of simple percentage, technically known as Com- 
mission, Broherage, and Profit and Loss, following the 
same order and with the same analysis as in the four 
cases of simple percentage. 

Those who prefer to do so may readily combine these 
divisions under the general head of ^^ percentage not in- 
volving time.^^ 

The third division of the subject is interest, or "per- 
centage involving time.'^ It has five cases — one funda- 
mental and four derived. 

In treating the percentage rules many skillful teach- 
ers prefer to introduce algebraic formulas, in which the 
initial letters of the several terms employed in percen- 
tage are the elements. To this course there is no ob- 
jection, provided that the formulae be not employed in 
the mental arithmetic, and that they accompany the 



ABITHMETIG. 207 

usual analysis and be not used as a sitbstititte for it. 
With this exception, the processes and explanations of 
the mental arithmetic should not differ from those of 
the written arithmetic, the chief distinction between 
the two being, that in the latter the numbers are too 
large to be carried in the mind. 

The subject of arithmetic being necessarily to a 
great extent cumulative, the teacher of this grade is 
especially advised to read over the directions given in the 
preceding grades, and in particular the table on page 
162. For the sake of brevity, the terms base, percent- 
age, etc., are employed in the following syllabus of top- 
ics in the usual technical sense of the text-books. 

Syllabus of Topics. 

The term percentage — exercises in reading per cent. 

Examples — Read the following, exemplified and defined first 
as decimal fractions, and then as per cent. : .75, .8, .605, .003, 
.08J, .001, etc. 

Exercises in changing common fractions to per cent, and 

mce versa : 

Examples— i f, ^§8, f|, 2|-, Ift, If, etc., how many hun- 
dredths ? what per cent. ? 

Examples— 25 per cent., 75 per cent, 33^ per cent, 14f per 
cent., 88f per cent., 325 per cent., 137i per cent., etc., are equiv- 
alent to what common fractions ? 

Note.— The common business fractions, halves, thirds, etc., to twelfths, 
inclusive, should be reduced to per cent., and the pupils made thoroughly 
familiar with them. 

SIMTLE PERCENTAGE. 

1st Case {Fundamental),— To find the percentage^ the base and 
rate being given. 

See table, page 162.— To find a given fi-actional part of a 
given number. 



208 HOW TO TEACH 

Examples— How much is 9 per cent, of 750 ? Had $750 in 
the bank ; drew out 9 per cent. How much was it ? 
Analysis as in the multiplication of decimal fractions. 

Note.— When this form of the case has been taught, its modifications 
should immediately follow. 

Example — Had $750 ; paid out 9 per cent. How much had 
Heft? 

Example — Had $750 ; earned 9 per cent. more. How much 
had I then ? 

2d Case (Derived). — To find the rate when the percentage and 
base are given. 

See table, page 162. — Tofind what fraction one given number 
is of another given number. 

Examples — 140 is what per cent, of 400 ? 

" Had 400 sheep ; sold 140. What per cent, did I 

sell? 

Analysis as in reducing a common fraction to a decimal frac- 
tion whose denominator is hundredths. 

Modifications of Case 2d : 

Example — I had 400 sheep ; I now have 540. What is the 
per cent, of increase ? 

Example — I had 400 sheep ; I now have only 260. What is 
the per cent, of decrease ? or, what per cent, have I left ? 

3d. Case {Derived), — To find the dase when the percentage and 
the rate are given. 

See table, page 162. — To find the number of which another 
number is a given fraction. 

Example — 140 is 35 per cent, of what number ? 

" Sold 140 sheep, which was 35 per cent, of my flock. 

How many had I at first ? 

Analysis as in simple fractions — 140 is i^o-o of what number ? 

Modifications of Case 3d : 

Example — Sold 140 sheep, which was 35 per cent, of my 
flock. How many had I left ? 

Example — Sold 140 sheep, and have 65 per cent, of my flock 
remaining. How many had I at first ? 

4th Case {Derived) — To find the base when the amount (or 
diflTerence) and rate are given. 

To find a number which differs by a given fractional part of 
itself from a given number. 



Analysis 
of last two ^ 
examples. 



ABITHMETia 209 

Example — What number 5s by 8 per cent, of itself more than 
351 ? or 351 is 8 per cent, more than what number ? 

Example — My flock of sheep increased 8 per cent.; I then had 
351. How many had I at first ? 

Example — I lost 8 per cent, of my sheep, and had 299 remain- 
ing. How many had I at first ? 

Note.— Axiom.— The base is 100 per cent, of itself. This is only a form of 

the fundamental axiom of fractions, 1— — 

n 

'First, find the per cent, of the base, represented 

by the given number ; 100 per cent. + 8 per cent. 

=108 per cent, of the base ; 100 per cent. — 8 per 

cent. =93 per cent, of the base. 

Second, proceed as in 3d case — 351 is ju I of what 

number ? — 299 is i^o^ of what number ? 

As a part of the general review, give an example in the fun- 
damental case, and let the pupils derive the other three cases 
from it, and then their modifications. 

Commission and Brokerage and Profit and Loss are but appli- 
cations of simple percentage. Each presents itself under all 
the four cases,but requires no special additional teaching, except 
in regard to the technical terms employed. 

Interest. — Teach the definitions of the terms employed ; the 
distinction of simple from compound interest ; the legal rate of 
U. S. and of the State in which the school is situated. 

Note.— In classes of an average character, one good method, in solving ex- 
amples in interest, will be found to give better results than two or more. 
Whatever method be employed, the pupils should, from the first, be carefully 
guarded against considering and calling the multiplier a concrete number. 
For instance, multiplying $15, the interest for 1 year, by 3 years ^ etc., is, of 
course, an absurd statement. 

If the six per cent, method be employed, it should be carefully 
analyzed, and the pupils should not be allowed to sacrifice 
sense to conciseness by such statements as " the half of 7 months 
is 3 cents-and-a-half "—one-sixth of 24 days is 3 mills, etc., etc. 
As a preliminary to applying this method, the class should have 
a thorough training on such questions as the following : Find 
.207 of $185.75 ; find .0685 of $36.25 ; (see preceding grade).— In 
2 years, 3 months, and 20 days, at 6 per cent, per annum, what 
decimal fraction of tlie 'principal is equal to the interest ? at 7 per 
cent? at 5? at 8? at7i?etc. 



210 HOW TO TEACH 

Give examples involving the various forms of the difference 
of dates— the application of the six per cent, method to a given 
or ascertained number of days. Example : Interest of $340 from 
Jan. 5th to July 3d, at 6 per cent. Examples involving the 
method when the year is estimated to consist of 365 days, should 
also be given. 

Give examples in Bank Discount, and explain its similarity 
to Compound Interest in being the interest on the amount. 

Note— (On the derived ca^es of simple interest.)— In teaching the four 
derived cases of simple interest, begin with an easy example in the funda- 
mental case, and from that derive the others in their order, being particu- 
larly careful to teach that, being derived, they all require division; that, to 
find the rate, the given interest is to be divided by the interest of the given 
principal at 1 per cent.; to find the time, by the interest of the given prin- 
cipal for 1 year ; to find the principal, by the interest of a principal of $1 ; 
and that, in the fifth case, the given amount is to be divided by the amount 
of $1. 

Give examples in True Discount, distinguishing carefully its 
difference in principle, and therefore of method, from Bank and 
Commercial Discount 

Partial Payments and Compound Interest should be very 
briefly treated, and with very simple examples. 

The form and nature of a promissory note, and the meaning 
of the several terms applicable to it, and the form of bills and 
receipts are included in the work of this grade. 



GEOGRAPHY AND HISTORY. 

Geography. — Complete the local and descriptive 
geography of one continent or grand division before 
beginning that of another. The same general plan 
should be pursued as in the preceding grades. If the 
prominent physical features of Asia, for instance, be 
first taught as a whole, including the climate, the 
pointer and the outline map being used to expedite the 
process, the descriptive geography of the individual 
countries will involve but little labor, and will be 
easily remembered. 



HI8T0BT. 211 

The geography of Asia is by far the most important 
and interesting ; that of Africa and Oceanica is com- 
paratively simple, and should be reduced^ in teaching, 
to the narrowest liDiits that will give a clear view of 
the general physical conditions of surface and climate, 
and of the social conditions of the various races, to- 
gether with a knowledge of the leading productions and 
exports, and the location of the principal cities. 

Mevieiv. — The review should be as in the preced- 
ing grades. One of the most comprehensive and im- 
portant elements of a general review of the entire sub- 
ject is, to show the relations of Europe to all the other 
grand divisions of the globe, as to conquest, settlement, 
colony, language, etc. This may be taught in a very 
brief and general way, and is indispensable to a correct 
outline knowledge of the present condition of the 
human race, — one of the most important objects of the 
study of geography. 

JEEistory. — The teacher is particularly referred to 
the General Suggestions in regard to U. S. History, in 
the preceding grade. 

The Outlines of the Revolutionary War. — (Teach as 
in the French and Indian War.) 

Causes of the Eevolution. — Navigation Acts — Restriction of Co- 
lonial manufactures — effects of war on the national debt of Eng- 
land — taxation without representation — the Stamp Act, 1765 ; its 
nature — causes which led to its repeal — the Tea Tax — riot in 
Boston, 1770 — the Boston *' Tea Party/' its immediate causes, 
and its consequences — nature of the Port Bill, 1774— first Con- 
gress at Philadelphia — its measures — Lexington, April 19, 1775 — its 
effects upon the country— Bunker Hill — siege of Boston — Wash- 
ington appointed Commander-in-Chief— evacuation of Boston, 



212 HOW TO TEACH 

and subsequent general drift of military events towards the west 
and ^ouih— Declaration of Independence, July 4, 1776— battle of 
Long Island— its purposes and results— retreat to the Delaware 
—capture of the Hessians at Trenton— Princeton— La Fayette — 
British move on Philadelphia, 1777— Chad's Ford— its conse- 
quences— Burgoyne's invasion, its route and purpose, 1777— 
Schuyler— Burgoyne's disasters— Gates— the two battles of Still- 
water—Clinton's moYements—Burgoi/ne's surrender, October, 
1777— its far-reaching consequences— the French alliance and 
assistance— British retreat from Philadelphia— Battle of Mon- 
mouth, 1778— New York the base of the British— destruc lion 
along the coasts of Connecticut and Virginia— Wyoming— battle 
of the Chemung, 1779— it breaks forever the power of the Iro- 
quois— PaulJones— Charleston captured, 1780— large numbers of 
Tories in the south — consequent years of guerrilla warfare— Sum- 
ter — Marion— Gates at Camden — destruction of his army, and of 
Sumter's force — Arnold's treason — the mutiny at Morristown, 
1781 — its causes — condition of the army — Robert Morris — Ar- 
nold's ravages — Greene's retreat — battles in Carolina and their 
consequences — Cornwallis at Yorktown — combination of the 
French and American forces — Surrender of Cornwallis, October, 
1781 — its effects in America and in England — Treaty of Paris, 
1783 — its terms — condition -of the country at the close of the 
war. 

Articles of Confederation, 1776-1777-1781— the government 
before 1781— after 1781— Shays's rebellion, 1786— leads to a con- 
vention to revise the Articles — a new Constitution devised instead, 
1787 — adopted by the States — goes into operation, 1789. 

In the biographical remew include a brief notice of Henry, 
Hancock, Franklin, Lee, Jay, Livingston. 

1789-1797. — Washington's Administration — Domestic history; 
the cabinet — leading measures — States admitted — their former re- 
lations. Foreign reldiiioiis — Trouble with France, and its causes. 

Note 1 .—Bead the Indian war. The teacher will give a brief statement con- 
cerning Boone, Clark, the original extent of Virginia, and the Ordinance of 
178u 

TSoTE 2.— Give, orally, a very brief outline account of thePrench Revolution, 
the resulting relations of France and England and of Europe generally ; the 
continuance of these wars to 1815. Refer particularly to the fact that political 
differences in the United States were, to a great extent, based upon our foreign 



HISTORY, . 213 

policy, and that "We were at last drawn into the vortex of the great European 
wars in 1812. 

Refer also to Washington's Farewell Address, and give, briefly, a very few 
of its leading points. 

1797-1801. — Adams's Administration. — Foreign relations; — 
continued troubles with France. — Domestic history ; — unpopular 
measures — the death of Washington— removal of the Capital. 

1801-1809. — Jefferson's Administration. — Domestic history ; — 
admission of Ohio — its preyious relations — the Louisiana pur- 
chase — its immediate and subsequent importance — Hamilton 
and Burr, 1804 — a sketch of the history of each — Fulton's 
first steamboat, 1807. — Foreign relations; — Tripolitan war, 1801- 
1805, its causes and results. — {Read the detail.) The state of 
Europe, and the importance of our carrying-trade — extraor- 
dinary measures of France and England in relation to the 
rights of neutrals — English claims of right of search and im- 
pressment — bearing of the impressment claim upon our natural- 
ized citizens, and our national honor — " Once a subject, always 
a subject'' — affair of the Leopard and Chesapeake, 1807 — Or- 
ders in Council and the Milan Decree, 1807 — Embargo, 1807- 
1809 — Non-intercom-se Act, 1809. 

1809-1817. — Madison's Administration. — The entire interest 
centers in the Foreign relations— they control the Domestic history. 
Berlin Decree abolished, 1810, 

Note.— liead the affair of the Little Belt— Indian War. 

War declared June 19, 1812 — its two chief causes. 

'Note.— Bead the detail ol the military and naval operations ; show briefly, in 
outline, first, the several aggressive expeditions into Canada, from Detroit to 
the St. Lawrence— their general failure ; second, the smallness of the navy— its 
brilliant success, but little direct influence on the fortunes of the war, except- 
ing on the lakes— utter destruction of American commerce ; third, the aggres- 
sive expeditions of the British, the Americans being chiefly on the defensive 
after 1812— Indian war in the West and Southwest— invasions from Canada- 
blockade of all important ports— naval and military expedition against 
Washington and Baltimore— invasion by the way of Lake Champlain— expe- 
dition against New Orleans, and its purposes— final reptilse of all these at- 
tempts, and similar fate of renewed aggressions of the Americans against 
Canada— destruction of the Indian power. 

Give the sequelae of leading events, omitting the dates, except as to years. 

The Hartford Convention— its alleged purposes— its effects — 
treaty of peace, December, 1814— a part of the general pacifi- 



214 EOW TO TEACE 

cation of Europe upon the fall of Napoleon — the causes of the 
war not even alluded to in the treaty — have these questions 
ever been settled ? If so, when and how ? 

Note.— i?e<2c? the second Barbary war, 1812-1815— its causes and results. 

In the biographical review include a brief notice of Hamilton, 
Burr, Randolph, Fulton, Whitney, De Witt Clinton. 

1817-1825. — Monroe's Administration. — Domestic history ;— Mis- 
souri Compromise, 1820 — formation of new parties on questions 
of commerce and finaDce — Whigs and Democrats — the leading 
questions until 1845. — Foreign relations ; — purchase of Florida — 
the Monroe Doctrine, 1822, its origin and importance. 

1825-1829. — John Quincy Adams's Administration. — Tariff of 
1828 — leads to the defeat of the Whigs and the election of Jack- 
son. 

1829-1837. — Jackson's Administration. — Domestic history; — 
United States Bank — nullification, 1832 — Clay's Compromise. 
Foreign relations ; — the French indemnity. 

1837-1841. — Van Buren's Administration. — Panic of 1837 — Sub- 
Treasury Bill, 1840 — political revolution. 

1841-1845. — Harrison — Tyler'' s Administration. — Domestic his- 
tory ; — the Bankrupt Law — Dorr's Rebellion. — Foreign rela- 
tions ; — the Maine boundary — annexation of Texas. 

1845-1849. — Folk's Administration. — Domestic relations now 
give direction to Foreign policy^Oregon boundary — chain of 
causes leading to the Mexican war — boundary claimed by 
Texas— Mexican war. May, 1846, to Feb., 1848. 

Note.— i?eac? the details ; give the leading military events in sequence, 
omitting all dates, excepting years. Teach with the following grouping. 
Northern operations— Tsiylov east of the Rio Grande— west of it— Wool— Kear- 
ney— Doniphan— Fremont. Southern operations— ^coiV^ campaign. 

Treaty of Guadalupe Hidalgo — its terms — discovery of Cali- 
fornia gold in 1848 — its important subsequent influence upon 
the national development. 

1850-1853. — Taylor and Fillmore's Administi^ation. — The Slave- 
ry question the leading element in the subsequent history — the 
California question, 1850 — its alleged relation to the Missouri 
Compromise — death of Taylor — Clay's Compromise Bill, 1850. 

1853-1857.— P/^rc^'s Administration. — Effects of the Fugitive 
Slave Bill— the Kansas-Nebraska Bill, 1854 — it annuls the Mis- 



HISTORY. 215 

souri Compromise — rise of a new party, '' Free-soil " or Republi- 
can — civil war in Kansas, its causes — flow of immigrants into 
that territory. 

1857-1861. — Buchanan^ s Administration. — Continuation of the 
Kansas trouble — John Brown's affair — its effects — split of the 
great Democratic party — four Presidential candidates — election 
of Lincoln — extreme doctrine of State Eights — secession of 
South Carolina, Dec, 1860— Fort Sumter— more States secede — 
Confederate government formed, Feb., 1861. 

1861-1865. — Lincoln^ s Administration. — Civil war — Fort Sum- 
ter, April 12, 1861 — effects upon the North — the President's 
proclamation — more States secede, making eleven in all. 

I^OT^.—Bead the details of the war ; show the importance of the question 
of foreign intervention, and the efforts on both gides in regard to it. 

In the Review show that the operations of the Confederates were mainly- 
defensive, except in the great sorties of Lee at Antietam and Gettysburg, of 
Hood at Nashville, and of Early at Chambersburg— all of which were repelled. 
That the main objects of the aggressive movements of the Union troops were, 
]6t, the destruction of Lee's army; 2d, The opening of the Mississippi— that 
after the opening of that river by the fall of Forts Henry and Donelson, and 
the subsequent capture of New Orleans and Vicksburg, the lines were con- 
tracted by a movement from the northwest to the southeast, ending in Sher- 
man's march from Atlanta to Savannah and Goldsboro'. The leading inci- 
dents will then readily fall into place. — Show the importance of the blockade, 
the chief function of the fleet—also, but very briefly, the enormous expendi- 
ture of men and money on both sides, and the measures by which they were 
obtained. 

1865-1869. — Johnson's Administration. — Death of Lincoln — the 
two subjects of leading importance — 1st. Providing for the pub- 
lic debt — 2d. Reconstruction — the 13th Amendment — the 
President and Congress quarrel — impeachment — the French 
in Mexico, and the demand of the United States Government — 
purchase of Alaska — laying of the first Atlantic telegraph 
cable. 

1869-1873. — Granfs Administration.— 'F^ioi^c Railway — 14th 
and 15th Amendments — the Alabama question — leading pro- 
visions of the treaty of Washington — the Geneva Arbitration— 
the settlement of the northwest boundary question. 

Addenda — TKe rapid development of the country since 1815 
— the leading elements in that development — emigration and 
immigration — the Erie Canal and the Lakes as the great water- 



216 HOW TO TEACH 

•W2ij — Steam and steamboats — railways — telegrapns. In tlie 
biographical review include a notice of prominent men, such 
as Calhoun, Clay, Webster, Seward, Greeley, Morse, etc., etc. 



ELEMENTARY SCIENCE, 



cc 



Natural Philosophy. — The suggestion to use 

a simple text-book^' should not be interpreted as a 
recommendation to dispense with oral instruction in 
this branch. On the contrary, the proper use of the 
text-book is as an auxiliary, as a general guide to the 
teacher in the selection of subjects, and as an important 
help to the pupil in preparing at home for the recita- 
tion of a lesson which has been previously explained 
and illustrated in the class-room. 

Any system of procedure which omits this prelimi- 
nary oral instruction is certainly not w^orthy of the 
name of teacliing. The text-book should be indeed 
brief and simple, and its illustrations must necessarily 
be few. But the teacher should supply the further 
illustration and experiment which will certainly be 
found to be necessary ; it is also of especial importance 
that the pupils should themselves be in every way en- 
couraged and led to report such instances of the appli- 
cations of the principles they have been taught, as they 
can themselves discover in the phenomena and inci- 
dents of their daily life and experience, both in and out 
of school, so that, as far as possible, they- may form 
habits of observation and reflection. 

The teacher will find a wide difference in the readi- 
ness with which individual pupils will conceive and 
apply scientific principles. With a few, the bare state- 
ment of a principle will often enable them to point out 



ELEMENTARY SCIENCE. 217 

its simpler applications. The results of a certain order 
of experiments, and the simpler deductions from them, 
will be promptly anticipated by such minds. But it 
will not be so with all ; and with some, only by careful 
and repeated illustration will the principles which in- 
terpret the facts presented, be clearly apprehended. In 
all experiments the pupils themselves should be made 
as far as possible participants. In. reviews they should 
be called upon to repeat the experiments or statements 
made by the teacher or given in the text, and to give 
the proper explanation. They should also be encour- 
aged to try further experiments for themselves at home, 
and to furnish an account or a repetition of them in 
the class-room, if possible. 

The teacher should also particularly remember that 
it is not necessary to follow slavishly the exact order ox 
selection of topics given in the text-book. The teach- 
er, and not the book, should be the master. An intel- 
ligent pupil will not be long in finding out whether or 
not the statements in the text are the limit of his teach- 
er's acquisitions. The great majority of young minds 
are hungry for this sort of knowledge, and it will un- 
questionbly be the teacher's fault if that appetite be 
not at the same time both gratified and stimulated. 

Care should be taken, when the scientific meaning 
of a common term diff'ers greatly from the popular one, 
to point out clearly such difference, in order that the 
pupil be not misled by thinking that he knows that of 
which he is really ignorant. Among the many cases 
in which this will be found necessary, the terms poros- 
ity, porous, solid, and impenetrahility may be taken as 
instances. It is by no means necessary that the pupil 
should be able to give an exact and comprehensive sci- 
entific definitio7% of such terms; a few analytical ques- 

10 



218 ' HOW TO TEACH 

tions by the teacher will readily show if the subject is 
understood. 

When a lesson from the text-book is to be given for 
home study, it should first be carefully illustrated and 
explained. No teacher will be likely to do this as well 
as he should, if he giye the subject no thought until 
about to assign the lesson. After receiving these expla- 
nations the pupil will be far less liable to misconceive 
or, as sometimes happens, to fail utterly to comprehend 
the statements of the text. As far as the subject will 
allow, he should be led through the medium of experi- 
ment to a knowledge of W\^ facts. The facts once as- 
certained, the priiiciples underlying them may be de- 
duced. A limit will, sooner or later, be reached, where 
the more recondite parts of the subject, so far as they 
may be entered upon, must be taught empirically, in 
consequence of the pupil's limited knowledge of other 
departments of science. 

For instance, suppose that the teacher has already 
experimentally established in his pupil's mind a general 
idea of the terms force and gravity, and that he now 
wishes to lead him to know that ^' the weight of a body 
is the measure of ihQ force of gravity ^^ acting upon it, 
and after that to establish the law of its variation. 
Let the teacher or one of the pupils borrow a common 
spring-scale — the smaller and simpler the better — let a 
'^w^ilpull, and at the same time notice that he is ex- 
erting a force, that the position of the index will vary 
with the degree or amount of force, that the motion is in 
the direction of the force, however the instrument may 
be held ; now place a succession of heavy bodies in the 
scale, and let him notice tlaat the effects are identical 
with those produced by his muscular force. He will 
no longer vaguely conceive that the efiect produced 



ELEMENTARY SCIENCE, 219 

upon the scale is because the body is heavy (which was 
to him a vague term), but because the earth' actually 
pulls it as he did, though no connecting bond is yisible, 
as when he pulled. A knitting-needle suspended and 
balanced upon a thread and acted upon by a simple 
magnet, will clearly convince him that ^ force may bp 
exerted by one body upon another without actual con^ 
tact. You have clearly defined for him the idea that 
^' the weight of a body is the measure of the earth's at- 
traction upon it." If now you wish to teach the law 
of the variation of the weight of a body of invariable 
mass, as should indeed be done, the next step must be 
empirical. The pupil's deficiency in mathematics for- 
bids any other course of procedure. The ^^Law of 
Gravitation'^ must be ^^a^^^Z ^fo him, together with the 
reason for so doing without proof. It will develop in 
many a mind an earnest desire to supply that deficiency. 
The law of the variation of weight may now be readily 
deduced by first adding to the pupil's mathematical 
knowledge the technical meaning of the term squarCy 
'and then giving a variety of simple arithmetical prob- 
lems to illustrate it. 

There is, perhaps, no graver or more common error 
-in relation to this subject, among earnest teachers who 
are called upon to teach it, than the notion that this 
requires expensive or complicated apparatus. The very 
contrary is the case in the great majority of instances. 
Expensive apparatus, with its show of brass and glass, 
has a direct tendency to repress the most precious ele- 
ment and evidence of a teacher's success — experiment- 
ing at home by the pupils themselves. The principles 
of the lever may be just as well developed by means of 
a pen-handle, a pointer, or a window-pole, as by a pol- 
ished brass or steel bar ; a large spool makes an excel- 



220 ^OW TO TEACH 

lent wheel and axle; a ribbon-block a good single pul- 
ley^ fixed" or movable ; a slate, a book, or a shingle, an 
inclined plane ; a pocket-knife will soon furnish a good 
wedge from a little piece of board, while the use of the 
blade itself is an excellent illustration of the applica- 
tion of the principle; and a large screw or a discarded 
auger-bit, with a knitting-needle or a pen-holder for a 
lever, makes an efficient single screio. And so through 
every department of the subject. JSTothing marks more 
fully the ability of a teacher than fertility in such re- 
sources. Strings, tops, balls, and marbles; pop-guns, 
potato-mills, bean-shooters, and putty-blowers, and the 
thousand and one nameless articles to be found in pu- 
pils' pockets, furnish an exhaustless mine of apparatus, 
and good apparatus too, for the skillful teacher. The 
immortal Dalton wrought out his atomic chemical the- 
ory with apparatus which may be excelled in many a 
junk or old bottle shop ; and the teacher determined to 
succeed will find that ^' where there is a will there is a 
way/^ 

SYLLABUS OF TOPICS. 

(To he illustrated as far as possible ohjectively ) 

Constitution, Forms, and Properties of Matter. — Illus- 
trate the following terms — body or mass, molecule, atom ; solid, 
fluid, liquid, gas; sensible or cellular pores, as in bread or 
sponge ; physical or intermolecular pores, as in iron, water, air, 
and every form of matter ; porosity. 

Extension, impenetrabilit}^, rarity and density, compressibil- 
ity and expansibility, inertia, mobility. 

Force and its forms. — A ttraction and repulsion : refer brief- 
ly to the fact that atoms and atomic forces are treated of in chem- 
istry. Indestructibility of matter to be briefly explained. 

Molecular forces. — Cohesive force : the properties of matter 
which are dependent upon cohesion ; tenacity, flexibility, brittle- 
uess, hardness, ductility, malleability; the properties depend- 



ELEMENTARY SCIENCE. 221 

ent upon cohesion and molecular repulsion ; elasticity. Illustrate 
the elasticity of flexure ; of compression ; of expansion ; of tor- 
sion. Relations of solids, liquids, and gases to molecular attrac- 
tion and repulsion. 

AdJiesive force : properties dependent upon adhesion; capil- 
lary attraction and its uses in organic and iu organic nature. 

DimsiUlUy of matter — into particles by mechanical force; into 
molecules by heat, solution, etc. — What forces are overcome in 
each case, and by what other force. 

Mechanical force. — Gravity — why called universal gravita- 
tion ; its simplest phenomena ; its law ; weight, a measure of 
gravity. 

Mechanics op solids. — Center of gravity ; line of direction, 
plumb-line ; stable, unstable, and indifferent equilibrium. 

Simple MacJiines, — Lever, with simple problems in mental 
arithmetic ; pulley, wheel-and-axle, inclined plane, wedge, screw. 

Mechanics op liquids {Hydrostatics). — Mobility of liquids, 
and its cause; their small compressibility; pressure in every 
direction ; gravity the primary cause; equality of pressure at a 
given point ; variation of pressure with depth ; meaning of the 
term level; why still water has a level surface; why the hy- 
drant water flows from the open tap ; at what height it ceases to 
flow, and why ; other illustrations of the same principle ; what 
that principle is ; the hydrostatic paradox ; the hydraulic 
press ; specific gravity ; the hydrometer ; why iron ships float. 

Mechanics op gases {Pneumatics). — Air — its compressibility, 
expansibility, and elasticity; chief mechanical difference from 
liquids ; its weight ; its pressure in all directions ; upward press- 
ure and how shown ; the mercurial barometer, its construction, 
principle, and uses; Torricelli's experiment; Pascal's experi- 
ment ; the aneroid barometer ; height of the atmosphere, and 
gradual diminution of its density. 



Astronomy. — The teacher sliould, at first, en- 
deavor to awaken an interest in the subject by referring 
to some of the most impressive and beautiful phenom- 
ena connected with the sun, the moon, the stars, planets, 



322 S:OW TO TEAGH. 

comets, and -nieteors. He should endeavor to induce 
the pupils to observe more attentively these phenomena, 
and to excite their curiosity to know about them. En- 
courage them to ask questions in relation to what they 
observe ; as. Why does the moon change its appearance ? 
Why does the sun rise so far from the east point, or set 
so far from the west point at certain times in the year? 
What bright star was in the west on a certain night, at 
a particular time ? and other such questions, some of 
which the pupils are, of course, to be told cannot be 
answered until they have further studied the subject. 
Thus they will learn to study the science from nature 
as well as from the book. 

Let the general phenomena of the heavens be first 
explained ; the movements of the sun, moon, stars, and 
planets in relation to the horizon ; the circles of daily 
motion ; the difference between planets and fixed stars ; 
how to distinguish some of the former, etc. 

The following topics may then be taken up in their 
order: The Earth, its form, magnitude, motions, etc. ; 
Circles, and angular distances on the Earth and in the 
heavens; Day and Night ; the Seasons, etc: these topics 
should be illustrated by the use of a Tellurian, and 
Problems for the Globe should be used for the purpose 
of exercise and illustration. 

Next, teach the general arrangement of the Solar 
System. Inferior and superior planets — their magni- 
tudes, revolutions, position of orbits, periodic times, 
and apparent motions. 

The mathematical definitions necessary for the prop- 
er understanding of this portion of the subject should 
be taught incidentally thereto. 



FIRST GEADE. 

Tirne allowed, about twelve months. 
OUTLIiiTE COUESE. 



LANGUAGE. 

Reading f Spelling ^ Definitions^ and Word Anal^ 
psis, continued as in the preceding grade. 

English Grainmar.—AnsiljQis, Parsing, and Syntactical 
criticism and correction, continued; the anomalous and idio- 
matic forms to be taught and explained. 

Composition. — Exercises on selected themes ; Practice in 
Letter Writing, commercial and social. 

MATHEMATICS. 

Mental and Written Arithmetic. — Continued and re- 
viewed, including the rules pertaining to the mensuration of 
regular plane surfaces and solid bodies ; with exercises in anal- 
ysis and calculation, continued. 

Algebra.— 'Thiovigh. equations of the first degree. 

Geometry. — The geometry of plane figures, with practical 
applications. 

GEOGRAPHY AND HISTORY, 

Geography. — The Outlines of Physical Geography. 
Mistory. — The Outlines of Ancient and Modem. 



234 SOW TO TEACH 

ELEMENTARY SCIENCE. 

BY ORAL INSTRUCTION, OR WITH A SIMPLE TEXT BOOK. 

Natural JPhilosophy. — Simple outlines completed, to in- 
clude Acoustics, Pyronomics, Optics, Magnetism, and Electricity. 

A.stronomy. — Elementaiy, continued and completed. 

Chemistry. — Elementary principles and facts. 

WRITING AND DRAWING, 

Penmanship. — Instruction to be continued as in the preced- 
ing grade, with practice in the writing of paragraphs, verses, 
business forms, notes, superscriptions, etc. 

Drawing. — ^Drawing objects of regular form in perspective, 
block combinations, etc., with shading; copying pictures of fami- 
liar objects, animals, etc., with easy landscapes, as far as the 
time may permit ; also (for males) simple architectural and me- 
chanical drawing. 

MISCELLANEOUS BRANCHES. 

IBook-keeping. — Single and double entry ; with careful in- 
struction in the principles of the latter. 

Constitution of the United States.— 'RMovj of its adop- 
tion ; its various provisions and amendments ; the reasons for 
the same to be explained as far as may be necessary or appro- 
priate. 



GBAMMAR. 225 



How TO Teach 



SUBJECTS OF THE FIRST GRADE. 



LAXGUAGE. 

Heading^ Spelling ^ and Definitions. — See 

the preceding grade. 

English Grammar. — The exercises of this 
grade comprise those of analysis^ parsing, and com- 
position. Sentences of an irregular or idiomatic con- 
struction, should be presented to the pupil, with the 
•view to show how far their analysis can be made to 
harmonize with the usual syntactical rules, and to 
teach the just limits of their use. Anything bordering 
on sla7ig should be discountenanced and condemned. 
An improper construction — that is, one that contra- 
venes well-established rules and principles — should not 
be sanctioned by any ingenious analytical contriyance 
or substitution. 

The exercises in analysis should embrace the careful 
and critical study of select passages from some of the 
best English and American writers ; as Shakespeare, 
Milton, Pope, Cowper, Young, Bryant, Longfellow, etc., 
etc. Prose writers, such as Addison, Johnson, Irying, 
etc., should also be drawn upon for exercises, — always, 
however, with a critical end in view, — to discover and 
correct errors, as well as to find excellencies and beauties. 

Such exercises, to however limited an extent it is 
10* 



226 HOW TO TEACH 

possible to carry tliem, will always exert an important 
influence upon the pupils^ style of composition, if not of 
daily speech. They will serve, moreover, to cultivate the 
taste of the pupils, and to awaken an interest in their 
minds in the study of English and American literature. 
A good reading-book will be found an important auxili- 
ary in carrying on the instruction here suggested. 

Composition. — The exercises in composition in 
this grade, as in those preceding it, should be, to some 
extent, impromptu, so as to develop that fluency and 
readiness in the written expression of thought which is 
of so much service in almost every sphere of life. The 
writing of letters, etc., as suggested in the outline 
course, should receive a very careful attention at this 
stage of the pupils' progress. 



MATHEMATICS. 

Arithmetic^ — In this grade, the teaching of arith- 
metic consists in large part of a review of what has 
gone before, with exercises sufficient in number and dif- 
ficulty to familiarize the pupils with the principles, and 
render them expert and accurate in their application. 
For suggestions in regard to this part of the work, the 
teacher is referred to the preceding grades. 

The advanced work should comprise the following : 
Exchange, Equatio7i of Payments, Proportion, Partner- 
ship, Square Root, and Cule Root, with their simple 
applications, and Mensuration. The exercises em- 
ployed to teach these departments of arithmetic, should 
be of as practical a character as possible ; and all the 
processes should be specially analyzed, the rules given 



ARITHMETIC, 227 

being in all cases deduced from the analysis. A careful 
explanation of the business transactions involved in any 
of the rules or their applications, should always be given 
before the pupils are required to solve the problems. 
Failure more frequently arises from a want of this knowl- 
edge than from a deficiency in arithmetical attainment. 

The following syllabus contains a brief summary of 
what is suggested to be taught in this grade. 

Syllabus of Topics. 

Exchange. Its nature ; bills of exchange ; par of exchange ; 
acceptance ; domestic exchange — to include two cases : — 1. To 
find the cost of a draft when its face and the rate are given ; 2. 
To find the face, the cost and rate being given ; foreign exchange 
— including the consideration of bills on England and France 
(cases as in domestic exchange) ; analysis as in percentage. 

Note.— Remember that the old par value of the pound sterling is now 
prohibited by law, and that the new legal value is $4.866J^. 

Equa-tion op Payments. Cases : — 1. To find the average time 
of payment, when the items have the same date, but different 
credits ; 2. When the items have different dates ; 3. To find the 
average time for paying balance of account, having both debits 
and credits. Analysis^ on the principal of interest, reducing each 
principal concerned to $1. 

Proportion. Ratio ; proportion defined ; relation of ante- 
cedents and consequents ; ratio of 4 to 12, 4 : 12=:-i% ; method of 
finding the missing term ; simple and compound proportion dis- 
tinguished; problems involving each: these problems should 
be only such as are required to illustrate the principle, since 
they are ordinarily to be solved by analysis previously given. 

Partnership. Terms defined. Cases : — 1. To find each part- 
ner's share when the profit or loss is divided according to capital 
only ; 2. To find it when time is considered. Analysis, fractional, 
or by means of proportion. 

Square Root. Involution and evolution defined ; simple 
examples of each; powers of roots; illustration of what is 
meant by finding the square of a number ; what is meant by 



228 S:OW TO TEACH 

square root. Illustrate by simple powers, integral and fractional — 
common fractions and decimals (the latter carefully). Problems 
in which the root contains denominations other than units. Illus- 
trate by geometrical construction (square of the sum of two lines). 

The following are specimens of "simple applications/* which 
should be taught in this grade : — Given the area, to find the side 
of the square containing it. 

Given the length and width of a rectangle, to find the side of 
a square equivalent to it. 

Note.— In teaching the pupils how to find the area of a rectangle, avoid 
giving the eiToneous impression that we absolutely multiply the length by 
the width, as expressed by denominate numbers. Show that the number of 
superficial units corresponding to the linear units of the length, is multiplied 
by the number (abstract) of linear units in the width. Thus, if the length be 
10 feet, and the width 5 feet, the area must be, not 5 feet times 10 feet, but 
5 times 10 square feet, equal to 50 square feet. 

Given any two sides of a right-angled triangle, to find the 
other side. Teach and illustrate the geometrical theorem on 
which this problem depends. Give various questions requu*ing 
an application of this problem. 

Cube Eoot. How to extract it, with an illustration of the 
process. This is best given by means of the blocks constructed 
for that purpose. If the pupil has studied Algebra sufiiciently, 
a demonstration by the Binomial Theorem may be given. The 
formula representing the cube of the sum of two quantities, will 
enable the pupil to remember clearly the details of the rule. 

The applications of the Cube Root should include the com- 
putation of the contents of similar solids. 

Mensuration. This should at least include the following 
cases:— 1. To find the area of a parallelogram when the base 
and altitude are given; 2. To find the area of other quadri- 
laterals, with sufficient data ; 3. To find the area of triangles ; 
4. To find the area of a circle ; 5. To find the diameter and 
circumference of a circle when the area is given ; 6. To find the 
solid contents, from sufficient data, of a cube, parallelopiped, 
prism, pyramid, cylinder, cone, and sphere ; 7. To find the con- 
tents of a cask, or other vessel, with the requisite data. 

Every topic to be treated in the arithmetic of this 
grade should be introduced by corresponding mental 
exercises, the slate being used only when the numbers 



ALGEBBA, 229 

inyolyed are too large to be readily retained in the mind. 
The pupils should be very frequently practiced in this 
mental work. The text-iooh in mental arithmetic should 
be sparingly used, and great care should be exercised in 
assigning lessons for home-study in this branch. 

Algebra. — This subject should be taught as a pe- 
culiar mathematical language, by means of which the 
relations of quantities and the results of their combina- 
tions may be expressed, and thus the reasoning in re- 
gard to them facilitated. The symbols, both of quanti- 
ties and relations, or operations, should at first be care- 
fully taught and illustrated. 

The simple operations of addition, subtraction, mul- 
tiplication, and diyision, should not be exhaustively 
treated, as is usually done, before the pupil is made 
acquainted with the nature and use of equations. The 
equation is to algebra w^hat the proposition is to ordi- 
nary language. It is the means of definitely expressing 
a mathematical truth, either particular or general. In- 
equations (technically so called) express truths, but not 
exactly; as, when we say, a; +2/ 7 5, we do not indicate 
Tiow much the sum of x and y exceeds 5 ; but if we say, 
a; + 2/nr6, we express a precise fact. It is suggested, 
therefore, that equations be presented very soon after 
the preliminary explanation of the symbols employed. 
The examples of equations first presented should be of 
the simplest character ; and their use in the solution of 
problems should be objectively shown. This may be 
done by employing a few yery easy questions, such as 
are giyen in some of the text-books, for mental solution ; 
as, What number is that, to the half of which if 5 be 
added the sum will be 11 ? Eyen the dullest pupil can 
be easily made to perceiye the use of expressing that 



230 JB[OW TO TEACH 

condition so that it can be clearly kept in view ; as {x 
representing the unknown number) | + 5 = 11. 

In solving such a problem, the successive steps or pro- 
cesses of reasoning should be kept in view. Thus, sub- 
tracting 5 from each member, the result (expressed by a 
second equation) is, f=6; and, multiplying by 2 the 
result (expressed by a third equation) is x—12^ which 
gives the solution. (Applied axiom to be referred to.) 

Such an exercise, properly performed, will develop 
more intelligence than whole months of mechanically 
working out by blind rules long sums in addition, 
subtraction, multiplication, and division, such as Multi- 
ply x^ — dx-{-b by x^ — ^^ + 2 ; Divide x^ — y^ by x — y, etc., 
etc. These exercises are proper in their place, but of 
themselves they have but little, if any, educational or 
practical value. 

Syllabus of Topics. 

1. Preliminary explanation of symbols, both letters, as repre- 
sentatives of quantity, and the signs of relation or operation, as, 

H X -H = etc. ; exercises to familiarize the pupil with their 

significance and the mode of reading them. 

Note.— It will be of great service to accustom the pupil to read algebraic 
expressions in such a way as at once to indicate their meaning ; as, a +h, the 
the sum of a and 5; a—b^ the difference between a and b; axS, the product 
of a and b, etc. Exercises in finding the numerical value of expressions, 
•when particular values are attributed to the representative letters, will greatly 
aid in accomplishing this result. Thus, find the value of a2&— g>3 when a=3, 
5=2, c=l, etc. c 

2. Easy problems in arithmetic, the solutions of which may 
be facilitated by the use of equations, the latter to be of the 
simplest form, and involving only an application of the pupil's 
acquired knowledge of symbols. This will at once show the 
pupils the value of the algebraic notation, and interest them in 
the study of the subject, as being of practical value. 

3. Mental practice in solving such problems, by means of equa- 
tions. Most of the text-books in use will aflord a sufficient variety. 



ALGEBRA, 231 

4. Practice in solving equations of this character ; each equa- 

X X 

tion to be read previously in the form of a problem ; as = 

3 8 
10 ; which may be read : 

What number is that one-third of which exceeds one-eighth 
ofitbylO? 

The method of clearing equations of fractions and transposition 
should be taught, not by applying mechanical rules, but as pro- 
cesses of analytical reasoning. Thus in the equation above 
given, the pupil will easily be made to perceive, that the multi- 
plication of both members by 24 will produce an equation with- 
out fractions. 

24x^ 24x 

(The intermediate step = 240 should be at first used.) 

3 8 

5. After the pupils have acquired a clear idea of the nature 
and use of equations, and some expertness in operating with 
those of a simple character, those of a more difficult or complex 
form should be presented, giving occasion for the use of the 
operations of addition, subtraction, multiplication, and division, 
which can then be more exhaustively treated, with sufficient 
practice on the part of the pupil. 

6. The nature of literal equations or general expressions should 
be then taught, and examples given, some of which may be 
made to involve an application of all these processes. 

Such as the following are suggested : 

(2.) 

(3.) 

(4.) 

a — b a + b 

(a + b)x (a — b)x ^ 

(5.) =1 

a— b a+b * 



X + a 


X — a 

— fl 


b 


c 


X — a 


X— b 


b 


— a 

a 


X— a2 


X — b2 
— rt 


b 


a 


X 


X 

-f 


a — b 


— 1 

a + b 


(a + b) X 


(a-b)x 



232 ^OW TO TEACH 

Such equations as the above involve much useful practice, not 
only in adding, subtracting, multiplying, and dividing, but also 
in fractions and in factoring. The latter should receive careful 
attention. 

6. The method of solving equations containing more than one 
unknown quantity — involving the Yavions methods of elimination 
— should follow this, and sufficient practice in the solution of prob- 
lems should also be afforded. The latter, with the preparation 
herein indicated, may be made a most important aid in training 
the mind to careful and exact analysis, and logical reasoning — 
perhaps the most important object, generally, of the study of 
this subject. 

Note.— This syllabus is not designed to be entirely exhaustive, but to afford 
hints as to the order and method of presenting the most important topics. 

Geometry. — This subject, from its extremely ab- 
struct character, is quite difficult for young students 
fully to comprehend. It is essential that the abstract 
ideas with which it is concerned should be developed 
in the minds of the pupils at the preliminary stage of 
the study. Unless this is done, they cannot be bene- 
fited by the instruction, nor, indeed, take any interest 
in it. They will, moreover, be wholly incapable of 
carrying on the processes of reasoning involved in the 
demonstrations, unless they clearly apprehend the na- 
ture of the truths to be proved, as well as of those as- 
sumed as premises, or arguments. 

The first idea to be developed is that of a solid, as 
conceived in geometry, involving three dimensions of 
extension; next, that of a surface, abstracted from the 
solid, involving ttvo dimensions ; next, that of a line, ab- 
stracted from the surface, involving 07ie dimeiision; 
and, lastly, that of a point, as indicative of a position 
in the line, or at either of its extremities, and involving 
no dimensio7is. These terms, reversing the order, should 
then be defined; namely, pointy line, surface, solid. 



GEOMETRY, 233 

Unless these fundamental conceptions are clearly and 
thoroughly impressed upon the minds of the pupils, 
no true progress can be made. 

The classification of lines and surfaces may then be 
taught, the fundamental idea used being that of direc- 
tion ; as of a straight line, never changing its direction ; 
a curve line, changing it at every point ; of a broken 
line, changing it at certain points. The classification 
of surfaces into plane, curved^ and hrolcen may be made 
in an analogous manner. 

With this, the idea of parallel lines may be made to 
harmonize by conceiving them as lying side ly side 
(literal meaning oi parallel) , and all in the same direc- 
tion, i. e.y tending to a point at an infinite distance, or 
tending to points, at a finite distance, which, wherever 
assumed, are at the same distance from each other (the 
latter may be the easier to develop at first). 

The idea of a plane angle should be made to harmo- 
nize with these conceptions of a straight line and par- 
allel lines, being conceived as expressing the difference 
in direction of two straight lines that meet at a point. 

Note— This, it will be seen, harmonizes with the idea of parallel lines, 
which tend to a point at an infinite distance, and hence never meet^ and can- 
not form an angle; while the straight lines that form an angle tend to a point 
at a finite distance, and meeting at that point, form the angle. 

The definitions of Geometry form the groundwork of 
the subject, constituting the basis upon which all the 
subsequent reasoning rests ; hence, it is very important 
that these definitions should be clearly understood and 
carefully committed to memory. 

It is desirable, before the pupils are required to study 
demonstrations, that the different methods of reaso7iing 
should be carefully explained, and that they should, to 
some extent, be exercised in the same. This can easily 
be done by bearing in mind that geometrical truths 



234 HOW TO TEACH 

have reference to a comparison of magnitude, and hence 
involve the idea of equality as a definite fact, and ine- 
quality indefinitely. Thus, it is required to be proved 
that the sum of the three angles of a triangle is equal 
to two right angles ; also, that, of any two sides of a 
triangle, that which lies opposite to the greater angle 
is greater (not how much greater). Hence, as a pre- 
liminary exercise, the following might be given : — 
Question — If A is equal to B, and B is equal to C, how 
does A compare with C ? Answer — They are equal. 
Question — Why is A equal to C ? Answer — Because 
they are both equal to B. Question — How does that 
prove it ? Ansiuer — Because things that are equal to 
the same thing are equal to each other. Questio7i — 
Can that be proved? Answer — It cannot; it is self- 
evident. Question — What are self-evident truths called ? 
Answer — They are called axioms. 

A variety of such exercises may be employed ; and, 
in this way, the pupil, before beginning formal demon- 
strations, may be made clearly to apprehend the nature 
of geometrical reasoning — so different from that which 
he has generally employed during all his previous stud- 
ies, or which he is accustomed to use in daily life. If 
the foundation, as here suggested, is well laid, the pupil 
will soon find it as easy a task to read his geometry, 
and to learn it by reading (not rote study), as to read 
any other book of science. 

Of course, in hearing recitations in geometry, the 
teacher should vary the method, so as to preclude en- 
tirely the possibility of any rote study, or merely verbal 
recitation. For this purpose, the figures employed 
should be different from those in the text book, the 
letters used in connection with the figures should be 
changed, or numerals used in their stead. The demon- 



GEOMETRY. 235 

strations should sometimes be given without using 
either letters or numerals; and, in the case of such as 
are very easy, the figures themselves may be dispensed 
with. In most cases, the pupil should be required 
briefly to recapitulate the arguments employed. 

The amount of ground to be covered in this grade is 
defined as the " Geometry of Plane Figures/' The fol- 
lowing Syllabus (intended to be only suggestive) em- 
braces everything required. 

SyllabijS of Topics. 

I. Elementary definitions — axioms — symbols. 

II. Theorems relating to straight lines, angles, and polygons : 

1. The sum of any two adjacent angles is equal to two right angles. 

2. Vertical angles are equal to each other. 3. The various theo- 
rems pertaining to the angles formed by the intersection of two 
parallel lines and a third line. 4. Angles having their sides 
parallel are equal. 5. Triangles are equal, {a) when they have 
two sides and the included angle in each respectively equal ; {b) 
when they have two angles and the interj acent side in each re- 
spectively equal ; (c) when they have three sides in each respec- 
tively equal. 6. The sum of the three angles of a triangle is 
equal to two right angles. 7. The sum of the interior angles of 
a polygon is equal to twice as many right angles as the figure 
has sides, less four right angles. 8. The sum of the exterior 
angles of a polygon is equal to four right angles. 9. Theorems 
relating to a comparison of the perpendicular and oblique line 
drawn from the same point to the same straight line. 10. Only 
one perpendicular can be drawn from a given point to a given 
straight line. 11. The greater side of any triangle is opposite to 
the greater angle ; and the converse. 12. The opposite sides and 
angles of a parallelogram are equal ; and the converse. 13. Any 
problem, either after, or in connection with, these theorems, 
which can readily be performed ; as, to construct an equilateral tri- 
angle, to bisect a given straight line, or a given angle, etc. In 
order to aid in the solution of these, it will be necessary to teach 
the definition of a circle, its construction, and parts. 

Compass and ruler exercises may also be profitably interspersed. 



236 ICOW TO TEACH 

III. Ratio and Proportion, 

lY. The Circle: — 1. Belations of angles to chords, 2. Relations 
of angles to arcs, 

V. Area: 1. Comparative areas of parallelograms and of trian- 
gles. 2. Measure of areas^ of a parallelogram^ of a triangle, of a 
trapezoid y etc. 3. Of squares described on the sides of triangles. 

VI. Similarity of figures : 1. Of triangles. 2. Of polygons. 
YII. Problems, pertaining to the circle, the polygon, area, 

and similar figures. 
VIII. Practical applications in mensuration. (See arithmetic.) 

Outlines of Fhysical Geography. — Some 
departments of physical geograpliy, though perhaps not 
known to the pupil by that name, have always been the 
necessary introductory element to the most rudimentary 
outline of political geography. — Describing the course 
of a river, the position of a peninsula or a cape, the direc- 
tion of a mountain chain, or the boundaries of a conti- 
nent, is as truly a part of physical geography, as is the 
explanation of the oscillation of the tropical rain-belt, 
of the formation and transport of icebergs, or of the 
theories of the trade-winds and ocean-currents. 

The physical geography specially described in this 
grade is a comparative science. It considers the world 
as an organic whole, and includes the study of its plane- 
tary conditions, of the mutual relations of all its parts, in- 
ternal and external — the land, the sea, and the atmos- 
phere, — together with the geographical distribution and 
conditions of the various forms of vegetable and animal 
life, and of the various races of mankind. 

In the brief time that can be allowed to so compre- 
hensive a subject in a single grade, it is obvious that 
only the simplest outline can be presented. The work 
has been carefully prepared for in the geography of the 
preceding grades, to which attention is here specially 
invited. 



PHYSICAL OEOGBAPEY. 237 

A synopsis of the points included in the grade is here 
appended. If a text-book is used, the teacher should 
first de thoroughly familiar luith its contents, so that it 
may be employed principally as a reading or reference- 
book from which appropriate selections may be read in 
the class. If any other course be pursued, most of the 
text-books treat the subject so extensively that the pupil 
will necessarily leave it, at the end of the term, with 
only an unfinished foundation and no superstructure. 

Syllabus of Topics. 

The Earth as a Globe — its form and dimensions, and how as- 
certained. 

The Earth as a Planet — the zones, and their causes. 

The Interior of the Earth — its probable condition, and how in- 
ferred. (Treat briefly.) 

TJte Surface of the Earth — its division into land, water, and 
atmospheric envelope ; the land divided ; the ocean not ; co 
parative extent of land and water. 

The Land Surface — (Omit Geology). Comparison of the con- 
tinents in their direction, con torn*, elevations, and area ; compari- 
son of the great mountain systems of the continents; volca- 
noes ; distribution of ; theories of volcanic and earthquake phe- 
nomena (very brief); comparison of the plateau belts; of the great 
plains ; the great islands and archipelagoes, their distribution and 
arrangement. 

Note.— To illustrate the comparison of the continents by the several classes 
of elevations, give upon the blackboard rough chalk diagrams of sections of the 
continents. 

The Ocean — its subdivisions and great areas compared; its 
level ; its great currents, their function and some one theory of 
their origin (very brief) ; its tides and waves, and their effects. 
(Both very brief.) 

The Atmosphere— its constituents ; vital importance of its 
watery vapor and its carbonic acid to plants and animals ; evap- 
oration from the ocean surface, especially iu the torrid zone ; 
the atmosphere and the watery vapor as the Earth's blanket. 



238 HOW TO TEACH 

The Winds — the trades, aod counter-trades ; theory of (very 
brief) ; region of variable winds — (very brief) ; the winds as car- 
riers of ocean vapor ; solar heat the great cause of oceanic and 
atmospheric circulation. 

The Great Bain-belt-^its annual oscillations; tropical, rainy, 
and dry seasons ; the mountains as condens^'s — illustrations. 

Ih^ainage — the river systems of the several continents com- 
pared ; their existence and direction in relation to the winds and 
mountain ranges ; causes and location of deserts — illustration ; 
lakes ; snow in the frigid zone, and on lofty mountains in the 
torrid zone; glaciers, their origin and motion (very brief); ice- 
bergs, their origin. 

Vegetation (very brief) — warmth and moisture necessaiy to ; 
general characteristics of tropical vegetation ; examples of tropi- 
cal plants ; examples of plants of subtropical and temperate re- 
gions; of arctic regions; the great forest belts, their location 
and causes ; prairie belts ; desert belts ; effects of certain plants 
on human industries and development (very brief). 

Animals (very brief) — comparison of the characteristics of the 
several zones and continents as to animal life ; examples. 

Man — the various races, their numerical proportion, leading 
peculiarities, and distribution. 

The pictures and illustrative diagrams and maps of any good 
text-book will, if properly used, very greatly simplify and expe- 
dite the study of nearly every department of the subject, and 
will render definite ideas that might be otherwise vague. 



Sistory {Outlines of Ancient and Modern), — The 
general siiggestiojis given in relation to the history of 
the United States (see Third Grade) are, to a very great 
extent, applicable to this grade. The much greater ex- 
tent of time to be covered in teaching ancient and mod- 
ern history, together with the vast number and diversity 
of nations which it embraces, necessitates, in a much 
greater degree, the fixing of a good outline in the mind 
of the pupil, as preliminary to a more minute study of 
the subject. 



HISTOBY, 339 

This outline should be brief, but should show clearly 
the chronological and geographical relations of the na- 
tions, the history of which is to be studied, and, to 
some extent, their ethnological relations. When this 
has been done, it will be perfectly easy to take up the 
history of any nation comprehended in the outline, and 
to treat it intelligibly. 

The use of maps, charts, and synchronous tables, will 
aid yery much in impressing lirmly upon the pupil's 
mind such an outline as is here suggested. The maps 
used should show clearly and accurately the territorial 
extent and relations of the various nations generally 
treated of in ancient, mediaeval, and modern history. 
All names of places referred to should be carefully 
pointed out on the map, so that their exact location 
may be constantly kept in view. This will aid the 
memory very much, as it brings into play the faculty of 
conception. 

In the arrangement of topics the order of time should 
be carefully followed at first, and the date (year) of 
each important event kept before the mind of the pupil. 
A few lieading dates should be carefully memorized. 
After the history of different nations has been studied, 
the leading events of each should be arranged in syn- 
chronous tables. The reigns of contemporaneous sove- 
reigns, for example, should be compared, and the con- 
nection of events in each carefully studied. 

Eeviews, such as are suggested in connection with 
the United States history, by a chronological, geographi- 
cal, and biographical arrangement of topics, should be 
given with sufficient frequency. 

The following syllabus presents the topics which 
should be embraced in the outline above suggested : 



240 SOW TO TEACH 

Syllabus of Topics. 

1. The nations and countries of the most remote antiquity — 
Egypt and Ethiopia, Babylonia and Assyria^ Lydia, Media, Syria 
and Palestine, Persia. Of these only a brief sketch need be learned. 

2. Greece — the mythologic period (very brief) ; the period 
from the beginning of the Persian war to the Roman conquest of 
Greece. This will include the rise and fall of the Macedonian 
Empire, with its divisions under Alexander's successors. 

3. Rome — the legendary period ; the foundation of the Re- 
public in its various stages, including the contests between the 
orders of Patricians and Plebeians ; the successive wars with the 
Samnites, Carthaginians, etc. ; the civil wars, including the trium- 
virates ; the fall of the Republic, and the foundation of the Em- 
pire under Augustus. TUe territorial conquests should be shown 
in connection with this. 

4. The Roman Empire — its territorial acquisitions and chan- 
ges from Augustus to the division of the Empire at the death of 
Theodosius, including a brief sketch of the principal reigning 
emperors, and the invasions by the Goths, Huns, and Vandals. 

5. The Western Empire, from Honorius to its fall under 
Augustuius (brief), including the barbaric invasions. 

6. The Eastern EMPiRE—from Arcadius to the taking of 
Constantinople by the Ottomans ; a brief sketch, including the 
wars with the Goths, Saracens, Seljuks, Mongols, and Ottomans. 

7. The Saracenic Empire — a brief sketch of its foundation, 
its territorial conquests and extent, its divisions, and its fall. 

8. France— the invasion of Gaul by the Franks, and founda- 
tion of the Merovingian Dynasty ; a brief sketch of it; the Car- 
lovingian Dynasty, including Charlemagne's conquests, and the 
revival of the Western Empire ; the Capetian Dynasty to the end 
of the Reign of Louis XL This will include the Crusades. 

9. England— a brief sketch of British History before the 
time of Egbert ; from Egbert to the Tudors. (England maybe 
studied first, if it is preferred.) 

10. Other nations contemporaneous with England and France. 
(Very briefly.) 

11. Modern History — in a similar manner; England and 
France, as the leading nations; other nations, including Ger- 
many , Prussia, Russia, etc. 



ELEMEl^TAUT SCIENCE. Ml 

12. AiyiERTCAN History — not immediately connected with 
U. S. History. 

Other parts of the world as China, India^ etc,^ may be omitted 
in this preliminary outline — which is alf that can generally be 
pursued in the Common Schools. 

This history should be so studied as to induce the 
pupils to read standard writers upon the most impor- 
tant topics. The instruction should embrace advice 
and direction as to the best writers in each period and 
nation. Historical selections will be found yaluable for 
this purpose. 



ELEilENTAEY SCIENCE 
(by oral instruction or a simple text-book.) 

'Nattival PJiilosopJiy. — ^Eor general suggestions, 
see preceding grade. 

Syllabus of Topics. 

^C02^s^fc5.— Preliminary — a general idea of the transmission 
of vibrations illustrated — the nature of sound — sounding bod- 
ies — a medium necessary — the air as a medium — other media — 
limits of audibility of vibrations — velocity in air and other 
media — loudness does not alter the velocity — reflection of 
sound — echo, its causes and limits — physical distinction of 
noise from music — pitch in music — effects of tension upon 
vibrating wires — influence of sound boards— tuning-forks — 
speaking-trumpets, speaking-tubes — resonance — murmur of 
shell — the ear, its construction and action — the wonderful 
physical condition of the tympanum when listening to a full 
orchestra. 

Pyronomics. — Heat — known only by its effects — effect on the 
nerves — effect upon the constitution of bodies — transmission 
of heat — the three methods of transmission illustrated — air a 
bad conductor and worse radiator — important relation of this 
fact to clothing, to vegetation, etc. — heat as a sensation — rela- 
11 



243 HOW TO TEACH 

tion of terms hot and cold — sources of heat — quantity and effects 
of solar heat — its relations to physical geography — source 
of the heat developed by friction — motion of mass converted 
into molecular motion — heat only a mode of vibratory motion 
— force as indestructible as matter — source of heat in combus- 
tion — the thermometer — principles employed in its construc- 
tion — nature and determination of the zero — evaporation — its 
causes — effects on temperature of bodies — phenomena of boil- 
ing — temperature of boiling water — why invariable at a given 
elevation — economic applications — why the boiliug point varies 
with elevation — boiling in a closed vessel — the steam-engine — 
its essential elements and general principles — high-pressure and 
low-pressure engines. 

Optics. — Light — moves in straight lines — shadows — sources 
of light — ^vibratory nature of light (only refer to it) — velocity 
of light — how known — law of intensity illustrated — photome- 
try by shadows — non-luminous bodies — how seen — reflection — 
its law — mirrors, and their uses (treat more fully of the plane 
mirror than of the others) — refraction — its simplest phenomena 
— its law — lenses — uses of, especially the convex lens — color 
— the prism and the solar spectrum — the order of the colors 
(refer very briefly to thermic and actinic rays) — Frauenhofer's 
lines (brief) — phenomena of the rainbow — the colors of objects 
— primary colors — the eye and vision. 

Magnetism. — Magnets, natural and artificial — forms of artifi- 
cial magnets — polarity — attraction and repulsion — magnetic in- 
duction — temporary and permanent magnets — the Earth a mag- 
net — magnetic needle, and why it points to the north. 

Electricity. — Frictional electricity — conductors and non-con- 
ductors — electricity not a fluid but a polarizing force, related 
to magnetism — attraction and repulsion^electric induction — in- 
sulators — effects of points — atmospheric electricity — its origin — 
lightning-rods — the flash — the white hot air — the thunder — pop- 
ular fallacies as to electric fluids, thunder-bolts, heat-lightning, 
and the cause of thunder — current electricity from chemical 
action — a battery, its wires and poles — polarized condition of the 
parts — how to develop heat and light — uses made of these — sim. 
pie helix — simple galvanometer — magnetism developed by elec- 
tric current — temporary magnet and magnetic telegraph. 



ASTRONOMY, 243 

Astronomy. — The topics embraced in the preced- 
ing grade should be carefully reviewed in this grade, as 
far as may be necessary to secure thorough preparation 
for the advanced portions of the subject, which consti- 
tute the special work of the grade. The use of the 
globes should be continued, in order more fully to fa- 
miliarize the pupils with the Doctrine of the Sphere — so 
important to a clear understanding of astronomical facts. 

The interest of the pupils in the observation of astro- 
nomical phenomena should be sustained by calling their 
attention as frequently as possible to facts which they 
can verify in this way. By degrees, the pupils should 
be induced to familiarize themselves with the locations, 
at different seasons of the year, at a given time by the 
clock, of the most conspicuous constellations and stars. 
The use of the Celestial Globe, or a planisphere, • will 
furnish valuable aid in the accomplishment of this. 
The positions of the planets Jupiter, Saturn, Mars, 
Venus, and Mercury, among the stars, should be kept 
constantly in view, together with their apparent mo- 
tions, and general progress eastward. The use of a 
good almanac will afford assistance in accomplishing 
what is here suggested ; also in calling attention to 
the more unusual phenomena connected with eclipses. 

The following topics should be specially treated in 
this grade : 

Syllabus of Topics. 

1. The Sun — ^its magnitude, real and apparent ; distance from 
the earth (give a general idea of the manner of finding this, al- 
though a minute knowledge of parallax may be reserved for the 
more advanced part of the subject); solar spots — theory with 
regard to their cause, their apparent motions, what is deduced 
from this. Tlie Zodiacal light may be briefly referred to in connec- 
tion with the Sun. 

2. The Primary Planets — in succession, commencing with 



244 BOW TO TEACH 

Mercury, the pupil to learn the most important facts in relation 
to their orbits, magnitudes, telescopic appearance, synodic and 
sidereal periods, axial rotations, apparent motions, seasons, 
satellites, etc. The Asteroids, their orbits, etc. Any interesting 
facts in relation to the history of astronomical discoveiy should 
be communicated incidentally, as this will serve to make the 
subject more attractive. 

3. The Moon — in a similar manner, teaching about its phases 
and their cause, its revolutions, periods, Harvest Moon^ Librations, 
and a brief general description of the lunar surface {Selenog- 
raphy), 

4. Eclipses — solar and lunar ; total and partial, how caused ; 
comparative frequency — ecliptic limits. Transits, their cause — 
why important. 

5. Tides — flood and ebb, spring and neap, how caused ; prin- 
cipal facts connected with them ; the tidal wave ; height of tide 
at different places — primitive and derivative tides. 

6. Comets — their peculiar appearance, the different parts of 
which they are composed ; different kinds of comets ; periodic 
times of the comets of short period — interesting facts in relation 
to the orhitSy size, mass^ density, and apparent magnitude of con- 
spicuous comets. 

7. A brief account of Meteors, their supposed nature and origin 
— cause of the periodic displays of meteors. 

8. Staes — classification — the constellations — ^names, classifica- 
tion of, brightest stars in each — apparent change in position due 
Xo precession ; cause of precession ; exercises in finding the con- 
stellations visible at anytime ; the galaxy ; proper motion of the 
stars; multiple stars ; variable and temporary stars; distances of 
stars, how found ; parallax, diurnal and annual. 

9. Nebula — classification of; their nature and appearance; 
general location and appearance ; the location and appearance of 
the most noted. 

10. Time — how measured ; solar, sidereal, and civil day ; why 
the solar exceeds the sidereal day ; why the solar days are un- 
equal ; equation of time ; tropical, sidereal, and civil years, how 
and why they differ in length. 

11. Astronomical Refraction— its effect upon the apparent 
positions of the heavenly bodies ; variation at different altitudes. 

13. General Review. 



CHEMISTRY, 245 

In giving instruction in this subject, its special office 
as a means of training the conceptive faculty, should be 
kept steadily in view. Facts of observation and facts of 
inference should be carefully distinguished. Apparatus 
and diagrams will afford some aid in enabling the mind 
to grasp the more difficult facts of inference ; but the 
actual observation of the phenomena to be illustrated 
should precede, as far as possible, the use of these. 
Thus, a good tellurian will illustrate clearly the causes 
of the change of the seasons, and a diagram may be 
made to show the reason of their unequal duration ; but 
the facts of these changes and inequalities must first be 
clearly apprehended by the mind. If this is done, the 
natural curiosity to know the cause will make the pupils 
more attentive to the instruction given. Cumbrous 
and complicated machinery, without the attentive ob- 
servation of the natural phenomena, and the conceptions 
based upon them, rather serve to give false notions than 
to impart clear ideas of the actual facts. A good plani- 
sphere will prove a valuable aid in the study of uranog- 
raphy. 

Nor should the teacher fail, in connection with the 
instruction, incidentally to impress upon the pupil's 
mind that, in studying the laws of the universe, he is 
contemplating the works of a beneficent Creator, infi- 
nite in wisdom and power. No subject is so well quali- 
fied as astronomy to give just ideas in this respect, and, 
while performing a peculiar and most important office 
in the training and development of the intellectual pow- 
ers, to exalt the understanding and give elevation and 
tone to the whole character. 

CheTnistry. — The instruction given in chemistry 
in the common schools, like that given in physics and 



246 HOW TO TEACH 

in the natural sciences, must necessarily be at the most 
only rudimental. Whole sections of each subject must 
be omitted. In every department of oral instruction in 
science, the principal object should be to form the mind 
to proper habits of observation. This, together with 
the knowledge of the facts and principles of science 
incidentally thus imparted, is a preparation for the 
systematic study of these sciences, rather than a formal 
attempt to impart a knowledge of their complete out- 
lines. Yet this knowledge of the facts and principles 
thus obtained, is in itself of so great practical import- 
ance as to render it an indispensable part of any proper 
scheme of common school education. 

The process employed should, as far as practicable, 
be the same as that suggested for the instruction in 
natural philosophy. The lesson, when not a review, 
should usually begin with an experiment. The facts 
to which the attention of the pupils is particularly 
directed, should, as far as possible, relate to the chemis- 
try of common things or of every-day life. They should 
be so taught as to leave in the mind of the pupil a 
determination and a conscious ability to know more of 
a science so highly practical, so intensely interesting, 
and so obviously within his own power to acquire. 

As in Natural Philosophy, the greater part, or 
even the whole, of the necessary apparatus may, with 
a little ingenuity, be extemporized. As a stimulus to 
the inventive powers of the pupils, this is in itself an 
important matter in practical training, and will, per- 
haps more than anything else, insure the further prose- 
cution of the subject by the pupils themselves. There 
are so many excellent text-books in the rudiments of 
this science, all abounding with practical hints and 
illustrations, in relation to the construction of such 



CHEMISTRY, 247 

apparatus, that it is not necessary here to do more than 
refer to them. 

The following syllabus of topics, together with a few 
experimental illustrations therein introduced, is chiefly 
intended to show how the objective process of instruc- 
tion may be applied to the study of facts in chemistry, 
the subject being quite as profitably and easily approach- 
ed from any one of a dozen starting-points, other than 
the one here selected. No other department of science 
can be made to show the value of this process more 
clearly, or to furnish more important mental discipline. 
Experiment must be made to raise questions in the 
mind of the pupil, only to be answered by deductions 
from further experiment. 

A small portion only of the subject can here be suffi- 
ciently expanded to illustrate the process, the further 
details being necessarily left to the ingenuity of the 
teacher. 

Syllabus of Topics. 

Forces. — (Begin with a very brief review of the following 
points in Natural Philosophy.) All changes in matter are 
effected by forces ; examples of physical changes wrought by 
physical forces, in pulverizing, solution, fusion, polarization, etc., 
in which the substance remains unchanged in composition and 
general properties. 

Chemical changes ; those in which the substance has changed 
its properties ; experimental illustrations : (use no chemical 
names or terms at this stage of the work ; use well-known com- 
mon names as far as possible at first, such as sulphur, copper, 
blue vitriol, alcohol, etc.) 

Exp. 1st, Show copper filings and pulverized sulphur ; let the 
properties of each be objectively noted; melt them together 
slowly ; notice the heat given out in the process ; examine the 
substance produced by the combination ; it is neither copper 
nor sulphur ; compare with a similar mixture of melted sugar 
and sand ; solution will show these last unchanged. 



248 jb:ow to teach 

Exp. 2d, Burn sulphur in air ; the sulphur disappears, and an 
invisible sour gas is formed, perceived by the lungs and the 
smell ; has been made from the sulphur and the air. 

Exp. Sd. Burn alcohol or kerosene in air: show water as a 
product ; heat given out in all these changes of substance. 

Chemical attraction : such changes are produced by a force 
known as chemical attraction or chemical affinity : the atoms of 
sulphur and copper attracted each other and formed a new sub- 
stance ; (omit its name) ; this force frequently breaks old combi- 
nations to form new and stronger ones. 

Exp, 4t7i. Make a solution of blue vitriol (copper sulphate), in 
a small vial, dip a clean knife-blade into it ; copper is deposited 
on the blade ; ask what substance must have been contained in 
the transparent blue vitriol ; tell that this copper was combined 
with another substance which has taken up some of the iron, 
at the same time rejecting or throwing down a part of the 
copper. 

Elements (nearly all to be told) ; iron and sulphur called 
elements ; why ; there are many elements (65) ; some, like iron 
and copper are metals ; therefore called metallic elements; all the 
rest, like sulphur, are called non-metallic elements; about a 
dozen elements compose the greater part of the material of all 
known substances ; nearly every substance, water, rocks, plants, 
and animals consists of chemical compounds. 

Carbonic acid (carbonic dioxide ; carbonic anhydride ; use none 
of the names at first). What is it that bubbles in soda-water ? 
How do you know that it is not air ? Its taste ; its smell ; why 
called acid (reserve the scientific definition of an acid). 

Exp. 5th. Show marble fragments, or chalk (not the plaster 
cylinders used upon the blackboard). Show muriatic acid; 
dilute a little with water ; taste it ; an acid ; pour the dilute 
acid upon the marble or chalk. (A small bottle, bent tube, and 
receiving-bottle for the gas are necessary.) Smell the gas ; com- 
pare changes which have taken place with those of copper and 
the iron in Exp. 4 ; one acid has taken the place of the other ; 
the acid gas must have been solid ; the force which held it so 
compressed. 

Mcp. Qih. Burn a piece of marble or chalk in a charcoal fire ; 
lime kilns ; marble changed to lime ; properties difl'erent ; tell 
that the great heat has driven ofl' the gas. 



CHEMISTBY. 249 

Exp. *7th. Make and filter lime-water ; agitate some of the gas 
of Exp, 5 with lime-water in a bottle ; water becomes milky ; 
the gas has united with the lime as before burning ; chalky 
sediment settles ; lime water a test for this gas ; meaning of the 
term test, 

Exp. St7i, Agitate the gas from soda-water with lime-water: 
result identical with the last ; therefore the gas in soda-water is 
the same as that from the marble. 

Exp, 9th. Burn a candle in an open wide-mouthed jar ; close 
the jar tightly ; candle soon goes out; a part of the candle has 
disappeared ; test, as before, the air that is left in the jar ; there- 
fore the same gas. 

Exp, 10th. Let the burning candle smoke or smut white 
paper ; tell and show that the smut or lamp-black is charcoal ; 
its better name, carbon. 

Exp. 11th, Burn ordinary charcoal ; it seems to have dissolved 
in the air ; gather the air from it ; test it ; now use the popular 
name, carbonic acid gas (other and better names to be learned 
hereafter) ; therefore carbon in the candle ; in kerosene ; in all 
fats, coal, bread, wood, etc. Show by over-baked bread, meat, 
by wood, etc. 

Exp. 12th. Blow breath through a straw or a pipe stem into 
lime-water ; test shows abundant carbonic acid ; from bread, 
vegetables, and other food. 

Exp. ISth. Collect from marble a quantity of the gas ; show 
that it will not support combustion ; fatal to life ; the gas in 
mines, wells, vats, etc. ; suicide with charcoal ; necessity of 
thorough ventilation. 

In the same manner oxygen may now be considered, its 
properties and functions shown, and its principal compounds, 
including the carbonic acid of the preceding experiments. Hy- 
drogen, chlorine, and nitrogen may be next in order. 

Kevtew. At this stage it is desirable to review, rearrange, and 
explain the knowledge already acquired, under the following 
heads : 

Chemistry of water : hydrogen, oxygen ; solution of solids and 
gases in water ; hard and soft waters ; mineral waters. 

Chemistry of the atmosphere : combustion ; nitrogen ; carbonic 
acid ; its relations to plants and to animals ; illuminating gas. 

Chemistry of rocks and soils: limestone and lime; quartz, 

11* 



250 SO W TO TEACH 

sandstones, and silica ; clay, slate, and alumina ; granite, feld- 
spar, potash, soda, etc. ; common salt. 

Gheinistry of plants and animals : starch, gum, sugar, lignin, 
vegetable and animal oils, albumen, gluten, etc. 

Special topics : bread-making, soap-making, glass-making, fer- 
mentation, distillation, photography, etc., etc. 



MISCELLANEOUS BRANCHES. 

Soo'k -keeping. — After the forms required in 
single-entry book-keeping have been taught, which 
should be quite brief;, the nature of double-entry book- 
keeping should be explained, by showing the relation of 
deMt and credit, and how the former in one account 
may be exactly balanced in another, so that one set of 
entries may be made to verify the accuracy of another, 
and thus prevent the admission of any errors which 
may not be readily discovered and rectified. 

2. The classification of accounts should be followed 
by an explanation of the three books — Day-book, Jour- 
nal, and Ledger. Journalizing simple entries in the 
Day-book should then be taught; and sufficient exer- 
cises given to impart readiness and accuracy in the pro- 
cess. The keeping of a simple and brief set of accounts 
will then render the whole process and theory intelli- 
gible to the pupils' minds, and will also render them 
sufficiently expert in their application. 

3. All the common itisiness fo7'ms should be taught ; 
as the form of bills, receipts, bank checks, promissory 
notes, bills of exchange, invoices, etc., etc. Business 
correspondence should also receive some attention. It 
is of great importance to render the pupils expert in 
Avriting a good business letter. In every exercise 
fluency, legibility, and grace in penmanship should be 



MISCELLANEO US BBANCHE8, 251 

carefully attended to. Quantity and quality should both 
be insisted on in this respect. 

Constitution of the United States^ — ^The 
recommendation to teach the Constitution of the United 
States applies to pupils of both sexes in this grade. It 
would appear to be essential that those who pass 
through a full course for common schools should have 
some knowledge of the simple principles and require- 
ments of the organic law of the nation — the distri- 
bution of the powers of the general government, and 
the rights, duties, and obligations of an American 
citizen. 

The Constitution itself should be the text studied, 
the pupils being made familiar, as far as possible, with 
the language of the instrument, and also instructed in 
the meaning and intention of the several provisions. 
Several matters, purely technical, will need to be care- 
fully elucidated, such as ex-postfacto laws^ tills of at- 
taindei\ habeas corims, etc., etc. The history, English 
and American, particularly the former, with which 
these are connected, will prove a most instructive and 
interesting subject for comment by the teacher. 

Questions as to the construction of certain points in 
the Constitution, which have been in agitation at vari- 
ous times, during the past history of the country, would 
prove, in boys' classes especially, as far as time and op- 
portunity may admit, very beneficial for discussion, as 
tending to impart readiness m speech, as well as self- 
reliance and freedom in thought and opinion. 



252 £^0W TO TEACH. 



GENERAL SUGGESTIONS 

EeLATIYE to the ClASSIFICATIOK AIJTD I2!q-STIIUCTI02^ 

OF Pupils ik Schools. 

Reviews. — Such, a reyiew of previous lessons, in 
connection with each new lesson on the same subject, 
should be given as will cause the pupils properly to asso- 
ciate together the facts learned in all of them, and thus 
lead them to acquire a comprehensive as well as a famil- 
iar knowledge of each subject contamed in the grade or 
the course. 

General reviews of subjects should be had at least as 
often as once during each month ; and in these the lead- 
ing facts learned in previous grades should be included. 

Progress of Classes. — ^Whenever it is found that a 
class has advanced further in one or more subjects of its 
grade than it has in others, less time should be devoted 
to these subjects^ and more to others, so that the grade 
of the class may be equalized in all its studies. No 
study of a succeeding grade should be introduced into 
a class of a lower grade until the class has completed the 
requirements of the grade in all the branches of study 
included therein. 

Progress of Pupils. — It often happens that a 
few of tlie pupils of a class will so far outstrip their fel- 
lows in a single month, as to render it necessary to trans- 
fer these rapid learners to a class of the next higher 
grade. While great care should be exercised not to stimu- 
late the excessive mental activity or precocity of young 
pupils, yet the disparity of progress in pupils of the 
same class may sometimes be used as an incentive to 



GENERAL SUGGESTIONS, 253 

urge forward those who are extremely sluggish or inert. 
This may be done by promoting in a public manner, at 
the end of each month, two or three of the pui3ils ivho 
are found to have made the greatest improvement, into a 
higher class of the same grade. In doing this, however, 
care must be taken not to disturb the gradation by per- 
mitting pupils to omit important branches of study. As 
a general thing every pupil should be required to spend 
the whole time which may be prescribed for the grade. 

Heeitations. — No class in the primary grades 
should be required to spend more than half an hour, 
at one time, in the same exercise. The mind, as well 
as the body, needs rest. A change of subject, and a 
change in the manner of conducting class exercises, 
are both necessary in order to furnish opportunities for 
rest during school hours. 

The recitations should be spirited exercises. The 
questions should be as definite as possible. The teacher 
should carefully avoid implying in the question any of 
the facts or principles that should be stated directly by 
the pupil. The habit of repeating the pupil's answer 
should also be avoided. Pupils should be invariably 
required to use natural and proper tones in recitation, 
to enunciate distinctly, and to avoid grammatical errors. 
If this be not done, the lessons in reading and grammar 
will be of little avail to break up pernicious habits of 
speech, which the teacher, by his neglect, will have as- 
sisted to fix. 

Unless thoroughly familiar with the details of the 
text-book, the teacher needs special and renewed prep- 
aration quite as much as the pupils. Witholit this, 
he will not succeed. In hearing the recitations, he 
should carefully discriminate between the statements 



354 BOW TO TEACH. 

found in the text-book and additional ones which he 
may have found necessary to make in the preparatory 
explanation of the lesson, and which the pupil may have 
had no opportunity to con oyer. 

Lessons for Mome Study. — In every class, how- 
ever well graded, the pupils will differ much in age, 
health, mental capacity, and home advantages. A cor- 
rect and judicious classification will reduce this inequal- 
ity to a minimum; but there will still remain a wide 
field for the exercise of discrimination, care, and caution 
on the part of the class teacher. The lessons should, in 
all respects, be adapted to the average ability of the pupils 
of the class; but, even beyond this, some allowance will 
often have to be made in the case of pupils of quite in- 
ferior mental capacity or opportunities for home study. 
Teachers must bear in mind that the one great object 
of home study is to train the pupils to self-exertion, — 
to give them the ability to depend upon their own 
efforts as students, and by degrees, to dispense with the 
aid of a teacher. It is, therefore, of supreme impor- 
tance to avoid everything that would discourage, or de- 
prive of self-reliance ; and nothing has a stronger ten- 
den cy in this direction than the imposition of excessive 
tasks. 

Teachers are especially admonished to be considerate 
toward pupils of a delicate constitution, an over-excita- 
ble brain and nervous system, or in temporary ill-health. 
Many children of this class are precocious in mental 
activity and exceedingly ambitious to excel; and the 
greatest care is required to prevent them from injuring 
themselves by an inordinate devotion to books and 
study. 

The length of the tasks imposed should, therefore, be 



GENEBAL SUGGESTIONS. 255 

most carefully scrutinized and adjusted. The practice 
of assigning a fixed numler of words, lines, paragraphs, 
pages, or examples, without a minute inspection of their 
nature or contents, is often accompanied with disastrous 
results. The pupils are wearied and discouraged; and 
the parents, finding the work of the school-room trans- 
ferred to the home circle, lose all confidence in the 
judgment and ability of the teacher. 

The teacher should ascertain the methods which 
pupils employ in home-study. Verbatim study, except- 
ing in case of important definitions, is to be discouraged. 
While making the necessary preliminary explanations, 
a brief abstract of the leading points should be written 
upon the blackboard, and made the basis of the recita- 
tion. This will do much to induce a rational method 
in study, and prevent a slavish adherence to the text. 

The teacher should advise with his pupils as to their 
time and opportunities for home study. Household 
duties, cramped and noisy homes, and deficient light, 
no doubt greatly obstruct, in many cases, the pupils' 
efforts. These should be, as far as possible, ascertained 
and allowed for. Very small print should be entirely 
excluded from home lessons on account of its tendency 
to produce myopy, when studied by artificial light. 
Many hours of confinement in a crowded class-room, 
with the long-continued and close attention required 
there, renders rest and relaxation, with some kind of 
physical exercise, indispensable to growing boys and 
girls. The teacher should, at least, advise that these 
come before home-study. 

JPhysical Traini^ig. — The pupils should be ex- 
ercised, as much as may be practicable, in such a way 
as to expand the lungs, develop the muscular system. 



256 BOW TO TEACH, 

and impart an easy and graceful carriage to tbe body. 
In schools for boys, the marching drill should be em- 
ployed in the ordinary evolutions of the schools, with 
such instruction as may be requisite to make it efiec- 
tive. Light gymnastic and calisthenic exercises should be 
employed as far as may be necessary or suitable for the 
general objects of physical training, or as a pleasant and 
beneficial relaxation after the severer mental exercises. 

Where formal exercises in calisthenics, etc., are not 
employed, the pupils should have sufficient intermission 
for recreation in the play- ground. Time thus given to 
physical exercise will always prove a gain in the exer- 
cise of the mental powers. When pupils are under 
efficient discipline, their performances, at their lessons, 
are always better after exercise in the play-ground,— 
for the excitement, as it subsides, leaves the intellect 
more active and hence readier for class-room work. 

In the case of young pupils, even while in the class- 
room, it is desirable that they rise at intervals for a few 
minutes, to exercise, by varied movements, both the up- 
per and lower limbs. 

Manners andMorals^ — Such instruction should 
be given daily to the pupils of all the grades as will fos- 
ter a spirit of kindness and courtesy towards each other, 
a feeling of respect toward parent and teacher, and a 
love for cleanliness, order, law, and truth. The read- 
ing lessons and the ordinary incidents of the school- 
room may be made the means of inculcating the great 
moral truths common to all well-ordered minds. 

Children learn to love and practice kindness, neat- 
ness, truthfulness, and politeness by observing these 
traits in those around them. It is, therefore, exceed- 
ingly important that the teacher should present living 



GENERAL SUGGESTIONS. 257 

illustrations of these qualities, by her own conduct be- 
fore the pupils, during all her intercourse with the 
class. 

Social relations, the dependence of each individual 
upon his neighbor — the necessity of labor — the benefits 
of society and government, should be illustrated and 
taught by means of easy and familiar lessons suited to 
the age and capacity of the children. As the develop- 
ment of the moral nature is of greater importance to 
the welfare of the individual and the community than 
any other part of education, no opportunity should be 
omitted for training children in such habits as will 
cause them to grow up truthful, honest, self-governing, 
and law-abiding citizens. 



GOVERNMENT AND DISCIPLINE. 

In all the rules and methods of discipline employed, 
the true object of discipline should steadily be kept in 
view ; namely, to train the pupils so that they may form 
right habits. 

Firmness, vigilance, and uniformity, in dealing with 
children, are of the first importance. The teacher should 
never resort to violent means, as pushing, pulling, or 
shaking the children, in order to obtain their attention. 
All such practices constitute a kind of corporal punish- 
ment which, whether that species of coercion be per- 
mitted or not, should be most carefully avoided. 

Modes of punishment especially painful to the cor- 
poreal system, such as the sustaining of wearisome bur- 
dens, unnatural and long-continued attitudes of re- 
straint, standing, kneeling, etc., are exceedingly wrong- 
ful and injurious. Equally so is the confining of de- 



258 ^OW TO TEACH. 

linquents^ by tying them or shutting them in closets. 
These are all a resort to mere physical force, instead of 
moral incentives, and involye no appeal to a sense of 
honor or duty in the child. They do not properly as- 
sert the authority of the teacher, nor do they really pro- 
duce obedience on the part of the pupil. 

When corporal punishment is resorted to, it should 
be of a proper character — never partaking of that con- 
tinuous infliction of pain which we denominate torture, 
and never administered except in a spirit of mildness, 
and deep regret at its necessity. When all those per- 
suasive incentives and agencies which constitute 
moral suasion have been appealed to without avail, and 
there is no other recourse, corporal punishment may be 
resorted to in order to save the pupil, but for no other 
reason. The necessities of discipline may seem to re- 
quire it, and they certainly do, if in order to meet them 
the teacher must choose between chastising his pupil in 
this way and depriving him of the benefits of the school 
instruction and training, and thus insuring his moral 
destruction. 

In directing the various movements required of the 
pupils, care should be taken never to touch them: The 
teacher should take such a position before the class as 
will command the eye of every pupil, and thence direct 
by the voice, or by a signal. Pupils must be habituated 
to the impression that the teacher will give his com- 
mands but once, and that they must be obeyed at once. 

Harsh tones of the voice are unnecessary and im- 
proper. Words of disapprobation may be uttered by 
the teacher in a tone of decision, without the use of any 
severity that would imply resentment, anger, or antipa- 
thy on the part of the teacher. On the contrary, the 
language used, and the tones of the voice, should al- 



GENERAL SUGGESTIONS. 259 

ways express a feeling of sympatliy with the child. This 
is the way to win the youthful mind^ and to bend the 
will, through the affections ; a different course will an- 
tagonize it, and prevent all real submission, securing 
only a temporary semblance of obedience. 

" As is the teacher, so will be the school.^^ It is, there- 
fore, requisite that teachers should rigidly discipline 
themselves by carefully cultivating habits of neatness, 
cleanliness, and order, gentleness of manner, a watchful 
self-control, and a cheerful spirit. - In speaking, let the 
rising inflection of the voice prevail ; then, the falling in- 
flection of reproof will be more impressive and effectual. 

Teachers should seek to obtain the sympathetic regard 
of the children by giving a due attention to their wants 
and requests, which should be fulfilled as far as may be 
proper and reasonable. Children are quick to perceive 
and to resent injury or injustice. The child who asks 
for the privilege of a drink of water, for instance, may be 
suffering acutely ; and, if not accorded relief, when this 
seems to be perfectly practicable on the part of the teach- 
er, feels a sense of outrage which, for a time, if not per- 
manently, impairs its respect and regard for the teacher. 
The cultivation of a due feeling of sympathy for the 
children will wholly prevent this. The possession of 
this feeling in its fullness is the best foundation for suc- 
cess in both discipline and instruction. 

Encouragement inspires confidence; and children, 
more than others, need it. Let it be given in all cases 
where this can be honestly done. To a want of this in 
the discipline of classes, are to be ascribed the timidity 
and reserve so often manifested among pupils by a hes- 
itating manner, a low voice, and a tone of inquiry in 
response, especially to strangers. A proper degree of 
encouragement renders them confident and spirited, 



260 HOW TO TEACH, 

eager to tell what they know, and in an audible tone of 
voice. Encouragement has a peculiar influence in pro- 
moting both mental and moral improvement. 

Piiblic. exposures and ladges of disgrace belong to a 
class of punishments which, if ever resorted to, should 
be employed under careful limitations, and with great 
circumspection and prudence, for it requires a skillfuL 
discreet, and conscientious teacher to use them safely 
and with adyantage. \\\ the discipline of girls, they 
should be avoided altogether, as destructive of that nice 
sense of shame and that delicate sensibility to reputa- 
tion which are to be most carefully fostered in the fe- 
male character. 

Cleanliness^ metliod, and regularity are among the 
first and most necessary elements of popular education. 
Every rule requisite to maintain or impart these should 
be diligently and punctiliously enforced. 

Education is unfinished until the physical powers are 
brought into subjection to the understanding and the 
dictates of morality and social refinement. Children 
should be taught how to sit, to stand, to move, to walk. 
Eules are required for this ; but they need to be only few 
and simple, and the nice and watchful observation of 
children renders it quite easy to enforce them, provided 
they are not capriciously applied. Children must first 
be taught them, and then never permitted to yiolate 
them without admonition or correction. 

Teachers should never forget that their pupils are 
constantly and closely watching their conduct, and that 
they are prone to imitate whatever they observe. They 
should, therefore, see nothing that they may not safely 
imitate. There is an ^^unconscious tuition,^^ the silent 
infiuence of which produces the most permanent efiects. 

The character of children is greatly affected by their 



GENERAL SUGGESTIONS. 261 

surroundings. These should, therefore, be neat and or- 
derly. The rooms in which they assemble should be 
clean, the desks and other furniture, as far as possible, 
without injury or defacement, and everything giving 
evidence of constant and punctilious attention. Chil- 
dren, from the contemplation of these things, uncon- 
sciously acquire habits of order, neatness, and regular- 
ity, which have an important bearing upon their useful- 
ness and happiness in after life. 

The basis of good order is attention. It does not 
require that the pupils should occupy, for any certain 
time, a fixed position ; that they should be compelled 
to strain their glances upon a given point; that they 
should be as motionless as statues. All this is unnatu- 
ral ; and whatever is unnatural is really disorderly. 
The postures should be graceful, easy, and uniform, but 
should be frequently changed ; the movements, while 
as simultaneous as perfect attention would necessarily 
produce, should also be easy and natural. 

Good order involves impression rather than repres- 
sion ; it does not consist in a coercion from which 
result merely silence, and a vacant gaze of painful re- 
straint, but it results from the steady action of awa- 
kened and interested intellect, — -the kindling of an 
earnest purpose and an ambition to excel. Hence by 
making punishment the first, instead of the last, resort, 
the true object of educational discipline is defeated. 
The prevailing atmosphere of the class-room should be 
always that of kindness and love, equal to that of a 
parent, in whose place indeed the teacher is for the 
time; and it will be almost invariably found that every- 
thing essential to effective discipline will spring from 
an interchange of confidence and regard between teach- 
ers and the pupils committed to their instruction. 



362 liOW TO TEACH. 

Those who have the management and instruction of 
our Common Schools should exercise the greatest care 
that their teachings and influence be not exclusiyely in- 
tellectual, — that they tend not merely to inform the 
mind, but to form the character, — not only filling the 
head, but impressing likewise the heart. Even where 
the operations of these schools are confined to teachijig, 
let the kind of knowledge and the mode of imparting 
it be dictated by considerations having in view moral 
and religious, as well as intellectual, improvement. Let 
the knowledge imparted be always such as will refine, 
ennoble, elevate. When scientific truth is presented, 
let the pupil be led to look not simply at nature, but 
^^ through nature up to nature's God;^' let him learn 
the laws and phenomena of the physical universe with 
the spirit of the Psalmist, when he exclaimed, " When 
I consider the heavens, the work of thy fingers, the 
moon and the stars which thou hast ordained, what is 
man, that thou art mindful of him, and the son of man 
that thou regardest him ? '^ Thus may instruction in 
every class and grade be made effectual, without the 
dogmatic teaching of sectarian tenets, in subserving and 
promoting the best interests of its pupils, both temporal 
and eternal. Any scope or intention short of this would 
certainly be inconsistent with the intelligence, as well 
as the moral and religious character of our age and 
country, and must render our Common School educa- 
tion, as a means of fostering and supporting the free 
institutions of our Eepublic, unworthy of support or 
vindication. 



GENERAL SUGGESTIONS, 263 



A SCHOOL LIBRARY. 

Its Necessity. — Of all the means necessary to a 
teacher's true and lasting success in the mental and 
moral training of his pupils, few, if any, are equal in 
importance to a proper school library, — not necessarily 
a large library, or an expensive one, but a library con- 
sisting of interesting and instructiye books, such as boys 
and girls may readily be led to love to read. 

The pernicious character of the greater part of the 
cheap literature found in many so-called newspapers and 
in other cheap forms of publication, needs but little com- 
ment. Its enormous quantity shows that it is extensively 
read, and it is well known that it finds its chief market 
among the young. An enfeebled mind and a vitiated 
taste, as shown in a craving for exciting and unnatural 
stories, and in a positive dislike for instructive and truly 
interesting reading, as being too tame and insipid to 
hold the attention, are among the common and least 
injurious results of an unchecked indulgence in the men- 
tal dissipation which this trash induces. Its darker 
shades and more injurious and debasing consequences 
need not here be dwelt upon. The proper antidote and 
substitute for this wide-spread poison is good reading. 

Such a library is also the indispensable supplement to 
the systematic mental instruction given in the class- 
room. If, for instance, care be taken and opportunities 
sought during the lessons in geography, history, or in 
any of the departments of science, to introduce some 
little book from the library, and to read a few interesting 
paragraphs illustrating the lesson, a brief notice and 
commendation of the book at the close of the exercise, 
with a few hints as to how best to read it, will utilize 



264 BOW TO TEACH. 

many a valuable work that might otherwise remain un- 
touched upon the shelves. 

Once introduced into the world of good books, and 
fairly interested in even one of its many departments, — 
once tasting and enjoying the wholesome sweets of a 
sound and ennobling literature, a young man or a young 
woman, it may be safely trusted, will not abandon it for 
that to which allusion has been made. A teacher has 
failed in one of the most important of all of his func- 
tions, if, being in possession of a good school library, he 
has not fixed, in at least some of his pupils, the habits 
and love of self-culture, by leading them to become 
habitual readers. 

Its Character. — Great care and discretion are ne- 
cessary in the selection of books for a school library. As 
far as possible they should be S7naU loolcs. The greater 
part of the suitable works in history, biography, travels, 
etc., are readily selected, and should include such works 
as Abbott's Histories, Scribner's Library of Wonders and 
Library of Travel, Chaillu's works, the Eollo books, etc., 
together with a fair proportion of good standard w^orks, 
such as those of Prescott, Bancroft, Lossing, Hume, and 
Macaulay, the Student's Series of Histories, Translations 
of Josephus, Herodotus, Thucydides, etc. In selecting 
from the great number of works of imaginary travel and 
adventure, written with the professed purpose of giving 
to youth instruction in the physical geography, natural 
history, and social condition of various countries, all 
those in which the narrative is overdrawn, and there- 
fore teaches error, should be rejected. Natural history 
and the other subjects treated of in the oral instruction 
in science, should be abundantly represented. If works 
of fiction are admitted they should be selected with ref- 



OENEBAL SUGGESTIONS. . 265 

erence to their moral purity and their permanent yalue 
as additions to literature, rather than because they are 
new and are advertised as popular. Many a school li- 
brary has been filled with ephemeral trash and made the 
instrument of mental degradation rather than of eleva- 
tion, by want of care in this respect. Such old classics 
as Eobinson Crusoe, Paul and Virginia, and the Vicar 
of Wakefield, should not be wanting. A few of the lead- 
ing popular poets should also be represented by small 
volumes. In their selection of books, pupils should be 
advised by their teacher, so that they may not attempt 
works beyond their present ability to read with profit. 

ZTses. — Among the many ways which may be sug- 
gested for making a systematic use of the library as a 
means of culture, the following is given as an illustration: 

Let us suppose that some new books have been pur- 
chased, and that one of them is Abbott's Life of Madame 
Eoland, and that the teacher has himself first read it, or at 
least looked over it, and marked a few short but inter- 
esting passages. Before the class or before several of 
the higher grades assembled for the purpose, the teacher 
hangs the map of Europe. In a brief conversational 
lecture he states to the class or school a few of the lead- 
ing points in relation to France and Europe at the 
period referred to, then reads a brief but interesting 
selection or two from the first portion of the book, and 
commends the book to their notice. "With such an 
introduction many pupils will read the work, while 
without it they would not have thought of so doing. 
It will generally be found that history and biography 
are usually not read by the pupils because they have 
none of the preliminary conceptions relating to the 

subject which the method above indicated supplies. 
12 



266 SOW TO TEACH, 

Books of trayel present peculiar advantages for this 
method, and are among the most instructive portions of 
current literature. 

An excellent plan with individual and advanced pupils 
is for the teacher to select some interesting book, suflBi- 
ciently brief and simple, and in place of the usual exer- 
cise in composition, to require of the pupil an abstract 
of limited length, with the selection of a page or two of 
peculiar interest or importance, to be read aloud, with 
such explanation or remarks as the subject may suggest. 



TABLE OF PRIMARY SCHOOL GRADES. 267 






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Education, 

General Philology, Works of Eeference, 
Handbooks for Teachers, etc. 



A descriptive List of 
American, British, Grerman, French, 

and other 

Books and Periodicals. 




E. Stei^ex», 

22 & 24 Frankfort Street, NEW YORK. 
1876. 






^■' »^ 



PREFACE, 



In presenting this Catalogue to the special public for whom it is in- 
tended, I deem it due to myself to make a few observations. 

What I herewith offer, is an attempt at a Descriptive Catalogue of the more 
important Publications on Education, General Philology, and other subjects 
of special interest to American Teachers ; in other words, this list is but 
the firstlings of a somewhat larger Catalogue which I shall strive to make as 
complete as may prove to be desirable, in subsequent issues. For reasons 
which need not be here dwelt upon, I have also enumerated not only the 
more important books and periodicals belonging to the above-mentioned 
classes, published in Great Britain, but also those of Germany and France. 

However small the present list, the labor involved in its compilation has 
been very great. Any one even moderately acquainted with the task herein 
represented, will appreciate the difficulties which had to be met and over- 
come. 

My desire was to make even the first issue of this Catalogue as complete, 
accurate, and serviceable as possible. Short titles of the publications herein 
enumerated have been noted for years. These had to be verified when 
practicable. 

Publishers' and other Catalogues do not generally give full and accurate 
information concerning authors' Christian names, the title as printed on the 
title page, the number of volumes, size, number of pages, style of binding, 
illustrations, and other particulars respecting the several publications. 

These data I consider essential, and I saw that unless they could be ob- 
tained, I should be compelled to exclude absolutely the majority of the 
titles previously collected. 

Some three months ago, therefore, I sent out proof-sheets, to the number 
of 680, to authors, editors, librarians, publishers, booksellers, school 
officers and others who I thought might be able to aid me in the work. 
Of these there are many who, either as authors or publishers of certain 
works, are directly concerned. 

I was in hopes that my endeavors would meet with general support, but 
to the 680 copies of the proof-sheets sent by me, with a special request 



Copyright, 1876, by E. Steigeb. 



— Ill 



attached, I received TO answers in all. Six hundred and ten of those ad- 
dressed on the subject have not yet been heard from. Consequently, a very 
large number of works are not enumerated here, which, by a little trouble on 
the part of those applied to, might have been duly described and have found 
their place in the list ; while, for special reasons, many titles have been 
retained in spite of the imperfect data at command touching the works 
themselves. 

Of the gentlemen who answered me, six or eight aided me very materially 
by corrections, suggestions, additions, etc., and to them my best thanks are 
tendered. 

Notwithstanding the care bestowed, I cannot claim that the descriptive 
statements appended to the titles enumerated in this list, may in all cases be 
relied upon. These particulars have been, in many instances, gathered from 
the various sources of information within my reach — not from an actual in- 
spection of the books — and are, therefore, open to revision and completion. 

The plan followed in the compilation of the present Descriptive Catalogue 
differs in some respects from that of other bibliographers. While aiming at 
a detailed accuracy not generally deemed necessary, I strive to combine 
clearness with brevity by the use of certain Abbreviations. 

These may be divided into three classes. The first class embraces those 
used for the Christian names of authors, and are: 



Ah. 


for Ahi'aham 


G. 


for 


Ge<yrge 


Fa. 


for Faul 


Alb. 


*' Albert 


Gu. 


«« 


Giistavus 


F. 


ft 


Feter 


Al. 


*' Alexander 


Bl. 


(( 


Henry 


Fh. 


(t 


Fhilip 


And. 


" Andrew 


J, 


(< 


Isaac 


Mi. 


(S 


Bichard 


Arch. 


*' Archibald 


Ja. 


<< 


James 


Bo. 


<< 


Bobert 


Au. 


«' Austin 


Jl. 


<< 


Joel 


Bud. 


a 


Budolph 


Ben. 


" Benjamin 


J. 


*« 


John 


Bu, 


" 


Bufus 


€. 


" Charles 


Jo. 


(C 


Joseph 


S. 


<< 


Samuel 


Dan. 


'' Daniel 


Ju. 


(( 


Julius 


St. 


(( 


Stephen 


Dav. 


" David 


L. 


(( 


Lewis 


Tha. 


(f 


Thaddeus 


Eh. 


" Ebeneze^' 


Lou. 


<< 


Louis 


Til. 


(( 


Theodore 


Edm. 


" Edmund 


Matt. 


<( 


Matthias 


Tho. 


« 


Thomas 


Ed. 


" Edward 


Mil. 


(( 


Milton 


Wa. 


*' 


WaUer 


E. 


" Ernest 


Nathl. 


ti 


Nathaniel 


Wash. 


(< 


Washington 


Fran, 


" Fi'ancis 


m. 


(( 


Nicholas 


W. 


<( 


William 


Fr. 


" Fred&ric 


No. 


(( 


Noah 








Fri. 


" Friedrich 


Ol. 


(< 


Olivet^ 








Where a Christian name 


is unknown, or not usually written 


in 


full, the initial is 


followed by a colon (:). 















The method, generally adopted, of transposing the Christian and surnames 
of authors, has been departed from in this Catalogue, in order to render it 
uniform with all my other Catalogues, and also from the conviction that the 
difficulty, inherent in the other system, of distinguishing the two classes of 
names may, by the adoption of the present plan, be avoided. 

The second class of Abbreviations deals with the size of books, which 
they represent thus : 

fo.=Folio.— 4.=Quarto.— roy. 8. or imp. 8.=Large size Octavo.— cr. 8.=Crown 8.— 
8.=Octavo. — 12.=Duodecimo, etc. 

It will, of course, be understood that, unlesss otherwise stated, each work 
consists of but one volume, and that the description of the same refers to 
the last edition, i. e. the one now in the market. 



IV 



& 


and 


gt.e. 


gilt edge 


pp. 


bds. 


boards 


gt.s. 


gilt side 


pap. 


bo. 


bound 


gt.t. 


gilt top 


phots. 


cf. 


calf 


hf. 


half 


pL.pls. 


cl. 


cloth 


illd. 


illustrated 


pt., pts. 


col. 


colored 


ills. 


illustrations 


rev. ed. 


cop. pi. 


copper plate 


interl. 


interleaved with 


. ro. 


cop. pis. 


copper plates 




writing paper 


russ. 


dble. p. 


double page 


law sh. 


law sheep 


sh. 


e. 


edge 


1. 


leather 


sq. 


ed. 


edition 


lib. 


library 


St. 


eng., engs. 


engraving, — s 


lith., litbs. 


lithograph, — s 


tur. 


flex. 


flexible 


mp., mps. 


map, — s 


v., vs. 


full gt. 


full gilt 


mor. 


morocco 


wd. 


full p. 


full page 


obi. 


oblong 


wd. cts. 



The Abbreviations of the third class embrace every thing else descriptive 
of books, and signify: 

pages 

paper 

photographs 

plate, — s 

portrait, — s 

revised edition- 

roan 

Russia leather 

sheep 

square 

steel 

Turkey leather 

volume, — s 

wood 

wood cuts 

The several Abbreviations are used in this order : The figure following 
the title or the statement in regard to illustrations, etc. , indicates the size, 
and the figure following the perpendicular line ( | ) names the number of 
pages. Then follow successively the stjde of binding, price, and place of 
publication. — Where information could not be obtained, the space is left 
blank. 

With such imperfections as it may bear, I now send forth this new num- 
ber in the series of my Catalogues, and trust that these bibliographical labors 
may prove useful. I cherish the hope that all who can will aid me, by such 
information as they may have, in bringing subsequent editions of the 
"Pedagogical Library" to the completeness and perfection essential to the 
permanent utility and consequent value which are my chief aim in its 
production. 

In conclusion I would express my conviction, based upon observation 
and experience, that descriptive Book Catalogues stimulate the purchasing 
of books ; that they are beneficial to the student, whom they guide to the 
best means and helps, of which otherwise he might remain ignorant, no less 
than to the publisher, for whose books a demand is thereby created. 

There is among the productions of American publishers a much larger 
number of valuable books in special departments than is generally sup- 
posed. It is to be regretted that, owing simply to the want of proper, 
systematic cataloguing, their existence is unknown to thousands who might 
otherwise profit by them. 

New York, August 2d, 1876, JE. tSteigeV^ 



Education, General Philology, Works of Reference, 
Handbooks for Teachers, etc. 



nJac, Abbott. Gentle Measures in the Manage- 
ment and Training of the Young, or the 
Principles on which a firm Parental Author- 
ity may be established and maintained with- 
out violence or anger, and the Right Develop- 
ment of the Moral and Mental Capacities be 
promoted by methods in harmony with the 
Structure and Characteristics of the Juvenile 
Mind. A Book for the Parents of Young 
Children, illd. 12 1 cl. $1.75. N. Y. 

The Teacher. Moral Influences employed 

in the Instruction and Government of the 
Young, illd. 121 cl. $1.75. N. Y. 

jr. S: C: Abbott. The Child at Home; or, the 
Principles of Filial Duty familiarly illus- 
trated. illd. 16 1 cl. $1.00. N. Y. 

The Mother at Home ; or, the Principles of 

Maternal Duty, familiarly illustrated, illd. 
16 1 cl. $1.00. N. Y. 

Amos Bronson Alcott. Record of a School, 
exemplifying the Principles and Methods of 
Moral Culture. lQ\291.cl. $1.50. Boston 

tJb. Alden, Christian Ethics; or. The Sci- 
ence of Duty. 12 1 170. cl. $1.25. N. Y. 

Elements of Intellectual Philosophy. 121 

cl. $1.25. N. Y. 

• Hand-book for Sunday-School Teachers. 

161222. cl. $0.75. N. Y. 

Outlines on Teaching. 12 1 32. flex. cl. 

$0.25. N. Y. 

Arch. Alexander, Outlines of Moral Sci- 
ence. 12 1 cl. $1.50. N. Y. 

S, Davles Alexander, Princeton College 
during the Eighteenth Century. 81341. cl. 
$2.50. N. Y. 

Arch. Alison, Essays on the Nature and 
Principles of Taste. With Corrections and Im- 
provements by Ab. Mills. 12 | cl. $1.50. N. Y. 

•7; AUeker, Die Volksschule. Unter Mit- 
wirkung von Fachmdnnern herausgegeben. 
81862. pap. $3.50. Freiburg 

S. An, AUibone. Dictionary of English 
Literature, and British and American Au- 
thors, living and deceased. From the Earliest 
Times to the Middle of the 19th Century. 
Containing over 46,000 Articles (Authors). 
With 40 Indexes of Subjects. 3 vs. roy. 
"' cl. $22.50, sh. $25.50, hf. mor. ant. 



81 



$28.50, full mor. $45.00. Phila. 

A New Dictionary of Poetical Quotations, 

coveHng the entire field of British and Amer- 
ican Poetry, from the time of Chaucer to 
the present day. With a variety of useful 
Indices, and Authors and Subjects alpha- 
betically arranged. 81788. cl. $5.00, sh. 
$6.00, tur. ant. $10.00. Phila. 



TTie American Convent as a School for Protestant 
Children. 18 1 340. cl. $1.25. N. Y. 

American Educational Cyclopaedia. A Ref- 
erence Book for all Matters pertaining to 
Education, v. I. 8|292. pap. $1.50, cl. 
$2.00. N. Y. 

American Eloquence. A Cyclopedia of Amer- 
ican Eloquence. 2- vs. With fine St. pts. 8| 
cl. $7.00, sh. $8.00, hf. mor. $10.00, hf. cf. 
$10.00. N. Y. 

Andre. Etudes sur les progres de V education 
et sur les diveloppements de Vinstruction po- 
pulaire en France, depuis les temps les plus 
recules jusqu'd J. J. Rousseau. 121 pap. 
$1.40. Paris 

C. Anthonys Classical Dictionary. Contain- 
ing an account of the principal Proper 
Names mentioned in Ancient Authors, and 
intended to elucidate all the important points 
connected with the Geography, History, Biog- 
raphy, Mythology, and Fine Arts of the 
Greeks and Romans, together with an account 
of live Coins, Weights, and Measures of the 
Ancients, with Tabular Values of the same, 
roy. 8 1 sh. $6.00. N. Y. 

Antoine Arnauld, Logique de Port-Royal. 
Avec introduction et notes par M. Joubdain. 
121 pap. $1.00. Paris 

Matthew Arnold. Essays in Criticism. 161 
cl. $2.00. Boston 

A French Eton; or, Middle-Class Educa- 
tion a,nd the State. 81 $1.00. London 

Higher Schools and Universities in Ger- 
many. With a new Preface comparing the 
Policy of the Prussian Government towards 
Roman Catholic Education and Roman Cath- 
olicism with that of the English Government 
in Ireland, cr. 8| $2.00. London 

Neil Arnott. Observations on National Edu- 
cation. 12 1 cl. $0.75. London 

Roger Ascham, Tlie Schole Master. With 
copious Notes and a Glossary by J: E: B: 
Mayor. 12 | cl. $3.00. London 

JFri, Ascher, Die Erziehung der Jugend. 
Ein Handbuch fur Eltern und Erzieher. 
81228. cl. $1.60. Berlin 

A: M: Bacon, A Manual of Gesture. With 
100 Figures, embracing a complete System of 
Notation, with the Principles of Interpretation 
and Selections for practice. 12 1 260. cl. $1.75. 
Chicago 

Fran, Bacon, Essays with Annotations by 
Archbishop Whately. New Edition con- 
taining a Preface, Notes, and Glossarial In- 
dex, by 'P-.Y: Heakd. 8 1 641 cl. $3.50, hf. 
cf. $6.00, hf. tur., gt. t. $6.00, full mor. 
$9.00. Boston 



E. Steisor, s^a 6c S4r ITrankfort St., PTew Yorlc, 



(Education, fbencval Pnifofogy, iOorfts of flcfermcc, etc. 



Fran. !Bacon, Essays and Colours of Good 

and Evil. With Notes and Glossarial Index^ 

ly W: Aldis Wbight. 12 | cl. $1.25. 

London 
— — Tlie Students* Bacon. Essays, with An- 

notationshy Archhishop^YHATF.L.Y. cr. 81641. 

cl. $2.50; hf. cf. S4.50; hf. mor. $4.50; fuU 

mor. $6.00. Boston 
Al. Bain. Logic, Deductive and Inductive. 

12 1 cl. $2.00. N. Y. 

Mental Science : A Compendium of Psy- 
chology and History of Philosophy. 12 1 cl. 
$1.75. N. Y. 

Moral Science : A Compendium of Ethics. 

121337. cl. $1.75. N. Y. 

Mind and Body. The Theory of their 

Relations. 121 cl. $1.50. N. Y. 

The Senses and the Intellect. 81696. cl. 

$5.00. N.Y. 

Fri, BaUhorn, Grammatography. A Manual 
of Reference to the Alphabets of Ancient and 
Modern Languages, roy. 8|80. cl. $3.75 
London 

JBT. Barnard, American Pedagogy : Edu- 
cation f The School, and The Teacher, iJi Amer- 
ican Literature. 81608. cl. $3.50. Hartford 

— — American Teachers, Educators, and Bene- 
factors of Education. "With 130 pts. 5 vs. 
8 1 cl. per V. $3.50. Hartford 

Educational Aphorisms and Suggestions, 

Ancient and Modern. Parti. 8|202. cL 
$2.50. Hartford 

- Elementary and Secondary Instruction in 
the German States : Anhalt, Austria, Baden, 
Bavaria, Brunswick, Hannover, Hesse-Cas- 
sel, Hesse-Darmstadt, Liechtenstein, Lippe- 
Detmold, Lippe-Schaumhurg, Luxemburg omd 
Limburg, Mecklenburg - Schwerin, Mecklen- 
burg-Strelitz, Nassau, Oldenburg, Prussia, 
Beuss, Saxony, Saxe-Altenburg, Saxe-Coburg, 
Saxe - Meiningen, Saxe- Weimar, Waldeck, 
WUrttemberg, and the Free Cities, with a gen- 
eral Summary of the Educational Systems 
and Statistics for the whole of Germany. S\856. 
cl. $5.50. Hartford 

Elementary and Secondary Instruction in 

Switzerland {each of the 23 Cantons), France, 
Belgium, Holland, Denmark, Norway, and 
Sweden, Russia, Turkey, Greece, Italy, Por- 
tugal and Spain. 8 1 878. cl. $5.50. Hartford 

English Pedagogy : Education, The School, 

and The Teacher in English Literature. First 
Series : Ascham's Schole Master; Bacon, On 
Studies and Education, with Annotations by 
Whately ; Wotton's Apothegms on Educa- 
tion; Milton's Tractate on Education; Hart- 
lib's College of Agricidture ; Petty's Trade 
School ; Locke's Thoughts on Education ; 
Spencer's Education; Fuller's Good 
Schoolmaster; Goldsmith's Village School- 
master ; Sii, nstone's Schoolmistress. 81482. 
cl. $3.50. Hartford 

Second Series. 8|608. cl. $3.50. 

Hartford 

English Teachers, Educators, and Promot- 
ers of Education. H\ 55(5. cl. $3.50. Hartford 

French Teachers, Schools, and Pedagogy — 

Old and New. 81648. cl. $3.50. Hartford 



FL. Barnard, German Pedagogy: Educa- 
tion, The School, and The Teacher inGemnan 
Literature, {Abbenrode, Beneke, Diesterweg, 
Fichte, Frcebel, Goethe, Graser, Hencamp, 
Hentschel, Herbart, Hertz, Raumer, Riecke, 
Wichern.) 8 1 916. cl. $3.50. Hartford 

German Teachers and Educational Re- 
formers : Memoirs of Eminent Teachers and 
Educators, with contributions to the History 
of Education in Germany, 8 1586. cl. $3.50. 
Hartford 

Military and Naval Sclwols in France, 

Prussia, Bavaria, Italy, Russia, Holland, 
England, and the United States. 8 1 960. cl. 
$6.00. Hartford 

National Education. Systems, Institutions, 

and Statistics of Public Instruction in differ- 
ent Countries. Part I. Europe. — German 
States. 81916. cl. $5.50. Hartford 

— Part II. Europe. — Switzerland, 

France, Belgium, Holland, Denmark, Nor- 
way, Sweden, Russia, Turkey, Greece, Por- 
tugal, 811263. cl. $5.50. Hartford 

Pesta'ozzi and Pestalozziani'^m. Life, 

Educational Principles, and Me'hods of John 
Henry Pestalozzi ; with Biographical Sketches 
of several of his Assistants and Disciples. 
With pt. 2 Parts in 1 v. 81468. cl. $3.50. 
Hartford 

Pnmary Schools and Elementary Instruc- 
tion : Object Teaching and Oral Lessons on 
Social Science and Common Things and other 
Subjects and Methods of Primary Education 
in the Model and Training Schools of Great 
Britain. (Papers for the Teachers. Sec- 
ond Series.) 81544. cl. $3.00. Hartford 

School Codes. Constitutional Provisions 

respecting Education. State School Codes, and 
City School Regulations. 8 j cl. $3.00. Hart- 
ford 

Science and Art. Systems, Institutions, 

and Statistics of Scientific Instruction, Ap- 
plied to National Industries in different 
Countries, v. I. Austria, Baden, Bavaria, 
Brunswick, Free Cities, Hannover, Nassau, 
Prussia, Saxony, Saxon Principalities, WUrt- 
temberg, France, Belgium, Holland, Den- 
mark, Norway, Sweden, Russia. Switzerland, 
Italy. 81807. cl. 5.50. Hartford 

— True Student Life. Letters, Essays, and 
Thoughts on Studies and Conduct; Addressed 
to Young Persons by Men eminent in Litera- 
ture and Affairs. Second ed. 81552. cl. 
$3.50. Hartford 

— Principles, Plans, and Specifications for 
Structures for educational purposes. Revised 
ed. With 1000 ills. 81800. cl. $5.00. 
Hartford 

— Superior Instruction in different coun- 
tries : Universities of Germany, Past and 
Present; History of Higher Teaching in 
Athens, Rome, and Alexandria; Early 
Christian Schools; Universities of Bologna 
and Paris; Revival of Classical Studies in 
Italy, the Netherlands, etc. Present Condi- 
tion of Universities and Colleges in Europe 
and "the United States. 81896. cl. $5.50. 
Hartford 



E. JSteigrer, ^3 && ^4 I^"rsLl^li^o^t St., PCeTT Yorlc, 



^ducatton, ®enera( phifofogy, Movk$ of Itcfcrcnce, etc. 



Th. H, Barvau, Conseils sur I'iducation 
dans la familleetau college. 8| pap. $2.00. 
Paris 

Direction morale pour les instttuteurs. 18 1 

pap. $1.00. Paris 

Carl BartheVs Schul-Padagogik. Ein Harid- 
huchfUr angehende Schullehrer u. Schulrevi- 
soren, Neu bearbeitet von G: Wan jura. 
8 1 418. pap. $1.25. Breslau 

J". Bartlett, Familiar Quotations: Being an 
Attempt to trace to their Sources Passages and 
Phrases in Common Use. 16 1 cl. $3.00; hf. 
cf. $5.00 ; cf. $6.00 ; mor. antique $6.50 ; 
mor. extra $8.50. Boston 

J. Russell Bartlett, Dictionary of Amer- 
icanisms : a Glossary of Words and Phrases 
usually regarded as peculiar to the United 
States. 8 1 cl. $2.50. N. Y. 

tT. Bascom's Aesthetics ; or Science of Beauty. 
12 1 cl. $1.25. Boston 

The Philosophy of English Literature. 

Lectures delivered before the Lowell Institute, 

Boston 121 cl. $1.75. N. Y. 
Principles of Psychology. 12 1 350. cl. 

$1.75. N. Y. 

Science, Philosophy, and Religion. 121 

cl. $1.75. N. Y. 

S, P; Bates. Institute Lectures on Mental 
and Moral Culture. 12 1 460. cl. or hf. cl. 
$1.50. N. Y. 

Method of Teachers* Institutes and the 

Theory of Education. 121140. cl. $0.75. 
N. Y. 

M: Bautain. The Art of Extempore Speak- 
ing. Hints for the Pulpit, the Senate, and 
the Bar. Edited by a Member of the New 
York Bar. With Additions, Rules of Debate, 
etc. 121364. cl. $1.50. N. Y. 

XT: Bech, Die Schule in Wechselwirkung mil 
dem Leben. Blicke in die Vergangenheit, 
Gegenwart und Zukunft der Schulen. 8 1 282. 
pap. $1.70. Miinchen 

Catliarine E: Beecher. Educational Re- 
miniscences and Suggestions. 161276. cl. 
$1.00. N. Y. 

• Physiology and Calisthenics in Schools 

and Families. Over 100 ills. 161 cl. $1.00. 
N. Y. 

Woman's Profession as Mother and Edu- 
cator, with Vieivs in Opposition to Woman 
Suffrage. 12 J 223. $1.25. Phila. 

Adolf Beer und Franz Hochegger, Die 

Fortschritte des Unterrichtswesens in den 
CulturstaatenEuropa's. 3 vs. Wien 

1. Das Unterrichtswesen Frankreich's. 81 
pap. $5.00. 

II. Das Unterrichtswesen Russland's und 
Belgien's. 8 1 269. pap. 2.10. 
III. Das Unterrichtswesen der Schweiz. 81 
378. pap. $2.95. 

Pamelia Belding. Infant Class Manual. 
18 1 cl. $0.75. N. Y. 



Fri, Ed, Beneke, The Elements of Psychol- 
ogy, on the Principles of Beneke, Stated and 
Illustrated in a Simple and Popular Manner 
byG: Raue. Fourth ed. by Johann Gottlieb 
Dressler. Translated from the German. 
8| cl. $3.00. Oxford. 

Erziehungs- und Unterrichtslehre. Neu 

bearbeitet und mit Zusdtzen versehen von J: 
G: Dressler. 2 vs. cr. 8|919. pap. $5.00; 
hf. mor. $6.40. Berlin. 

Bericht uber osterreichisches Unterrichtswesen. 
Aus Anlass der Wedausstellung 1873 heraus- 
gegebenvon der Commission fUr die CoUectiv- 
Ausstellung des osterreichischen Unterrichts- 
Ministeriums. 2 vs. With 1 mp. and 24 
pis. cr. 8 1 302, 652. pap. $4.20. Wien 

G. BerJceley. Principles of Human Knowl- 
edge. With Prolegomena, and with Annota- 
tions, select, translated, and original, by 
C. P: Krauth. 8 1 424. cl. $3.00. Phila. 

Leopold Besser, Das Werden und Wachsen 
unserer Kinder. Ein Buch Uber Kindes- 
pjlege. 16 1 344. pap. $1.05; cl. $1.90. Berlin 

The Bible in the Public Schools.— Arguments in 
the case of John D. Minor et al. v. The Board 
of Education of the City of Cincinnati et al., 
in the Superior Court of Cincinnati, with the 
Opinions and Decision of the Court. 8 1 cl 
$2.00. Cincinnati 

Arguments of Messrs. Ramsey, Sage, and 

King, in the above case, in favor of the Use 
of the Bible. 8| pap. $0.50. Cincinnati 

Arguments of Messrs. Stallo, Hoadly, and 

Matthews in the above case, against the Use 
of the Bible. 8| pap. $0.50. Cincinnati 

J". Stuart Blackie, On Self-Culture— Intel- 
lectual, Physical, and Moral. A Vade-Mecum 
for Young Men and Students. 16 1 116. cl. 
$1.00. N. Y. 

W: H: J: Bleek. On the Origin of Language. 
Translated by Davidson. 8| pap. $0.50. 
N. Y. 

Agnes von Bohlen. Das Buch der Mutter 
fur Haus und Erziehung. 8 1370. pap. $1.70. 
Berlin 

E: Bolun. Die Sonntagsschule. Mit Geneh- 
migung des Evang. - Juther. Sonntagsschul- 
Vereins der Stadt New York und Umgegend 
herausgegeben. N. Y. 
Erster Cursus. 16|37. bds. $0.15 
Zweiter Cursus. 16162. bds. $0.20 
Dritter Cursus. 16 1 52. bds. $0.18 
Vierter Cursus. 16|68. bds. $0.20 
Fiinfter Cursus. 16|53. bds. $0.20 
Sechster (|18 , Siebenter f|19 u.Achter 
Cursus ( 121), together 16|58. bds. $0.20 
Leitfaden fur Lehrer. 16|20. bds. $0.12 
Ernst Bcehme. Des Sohnes Erziehung. Pd- 
dagogische Briefe an eine Mutter. 8|244. 
pap. $0.95. Dresden 
Karl Borniann. Pddagogik fur Volks- 
schullehrer, auf Grund der allgemeinen Be- 
stimmungen vom 15. October 1872, betreffend 
das Volksschul; Prdparanden und Seminar- 
wesen. 81309. pap. $1.70. Berlin 



E. ®tel»er, 23 & q^ Franls^fort St., 2Vew York. 



Education, ^emvat Pfeitotogn, Morfts of Hefermcc, dc. 



Karl Bormann. Schulkunde fur evange- 
lische Volksschullehrer auf Grand der preus- 
sischen Regulative vom 1., 2. und 3. October 
1854 uber Einrichtung des evangelischen 
Seminar-, Prdparanden- und Etementar- 
schul-Unterrichts bearbeitet. 4 vs. 8| pap. 
$4.00. Berlin 

; Ueber Erziehung und Unterricht. Vor- 

■ truge. cr. 8|285. pap. $1.25. Leipzig 

F: JSoiven, A Treatise on Logic; or the 
Laws of Pure Thought. 121460. cl. $2.00. 
Boston 

if: R: IBoyd, Eclectic Moral Philosophy. 
Prepared for Literary Institutions and Gen- 
eral Use. 12 1 cl. $1.50. N. Y. 

Anna C: JSracJcett, The Education of 
American Girls, considered in a iSeries of 
Essays. 12 1 cl. $1.75. N. Y. 

MicJiel Breal. Quelques mots sur Vinstruc- 
tion publiqu£ en France. 12 1 pap. $1.40. 
Paris 

E: Cobham JBj'ewer, The Dictionary of 
Phrase and Fable, cr. 811014. cl. $3.50; M. 
of. $6.00. Phila. 

C. Astor Bristed, Five Tears in an English 
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U education de Vhomme. Traduit de Valle- 

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Bilder zur edlen Pfege des Kindheitsiebens. 
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The Mother^s Book of Song. Two-part 

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Fri, Froehel. Les causeries de la mere. Poe- 
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cation du premier age, d'apres F. Frcebel, 
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Traite des facultes de Vdme, comprenant 

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Ueber Begrundung, Einrichtungund Ver- 

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nach 

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. Die Mutter als Erzieherin ihrer Tochter 

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Universal Knowledge. "With over 1200 wd. 
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W. Cave Thomas, Symmetrical Education; 
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Mind and Body. cr. 81 cl. $1.25. London 

W. Thompson. Outline of Laws of Thought. 
A treatise on Pure and Applied Logic, with 
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M: T/wrnley. True End of Education devel- 
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Ed. Thring, Education and School, cr. 81 
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eJ". Tlnihs, School-Days of Eminent Men. 12 1 
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«7. Todd. The Student's Manual, pt. 121 
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The Daughter at School. A Companion 

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Northampton 

The Sabbath School Teacher. Designed 

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I. Todhunter, The Conflict of Studies, and 
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Tou'le's Comprehensive School Record, for 
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On the Study of Words. 121 cl. $1.25 

London 

Proverbs and their Lessons. \2\ cl. $1.00. 

London 

Select Glossary of English Words used 

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$3.25. PMla. 

Jo. A: Turner, A Brief Treatise on Punc- 
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Tho, Twining, Technical Training. Being 
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Frl, Ueberweg. History of Philosophy. 
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Cheap Edition. 2 vs. 81 cl. $5.00. 

J"; L: Ussing, Darstellung des Erziehungs- 
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Noa/i Webster, An American Dictionary of 
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Colors, (5> Lessons on Length, 6: Solids and 
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22 Education, ®cneraf PRifofogy, llorfts of Hcfcrmcc, dc. 



I?'; G; Welch. Moral, Intellectual, and Phys- 
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W» Whewell. Influence of the History of 
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JJ; Qrant White, Words and their Uses, 
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S: H: White, The Addresses and Journal of 
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Life and Growth of Language. 12 1 cl. 

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School Economy. A Treatise on the Prep- 
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Erl, Wiehe, The Paradise of Childhood. A 
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pap. $3.00. Springfield 

Fri, Wieck, Piano and Song: How to Teach, 
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T; Wie.se, Die Bi^dung des Willens. 8179. 
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T: Wiese, Das hohere Schulwesen in Preusseii. 
Historisch-statistische Darstellung im Auf- 
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J: F: Th: Wohlfarth, Padagogisches Schatz- 
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und Unterricht. FiXr Eltern und Lehrer. 
81423. pap. $1.25 ; cl. gt. e $1.90. Leipzig 

Th. J): Woolsey, Helpful Thoughts for 
Young Men. 161 cl. $1.50. Boston 

tTo, Emerson Worcester, Dictionary of 
the English Language. 4 1 1786. sh. $10.00, 
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russ. $12.00, full tur. mor. $16.00, full 
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Comprehensive Dictionary . illd. 121 cl. 

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ills, and tables. 181310. $0.75, ro. flex. 
$0.85, tucks $1.00. Boston 

Academic Dictionary. \ cl. $2.25. Boston. 

Universal and Critical Dictionary . 8) cl. 

$4.37. Boston 

Ed, Zi: Youmans, The Culture demanded 
by Modern Life : A Series of Addresses and 
Arguments on the Claims of Scientific Edu- 
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Discipline in Education. 121 cl. $2.00. N Y. 

J, G, ZegUn. Praktische Winke iXber die 
Fortbildung des Lehrers im Amte. ZugJeich 
ein Wegweiser zur EinfUhrung in die pdda- 
gogische, volkstlmmliche und klassisclie Liter a- 
tur. cr. 8 | 492 pap. $2.50. Giitersloh 

Tuisco Zilh'r, Grundlegung zur Lehre vom 
erziehenden Unterricht. Noch ihrer wissen- 
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Seite entwickelt. cr. 81530. pap. $4.40. 
Leipzig 

Die Regierung der Kinder. FUr gebildett 

Aeltern, Lehrer und Studirende bearbeitet, 
cr. 81190. pap. $1.00. Leipzig 



E. StelsreiT, S3 Sc S^ Kranlilort St., T^e^v Yorlc 



Vacation, ®cneraf J^^fo^^Byj Morfes of Hcfercncc, etc. 23 



Periodicals. 



AUgemeine deutsche Lehrer - Zeitung. Ber- 
THELT. 5214. With Supplement Anzeiger 
fur die neueste pddagogische Literatur. 
Stcetz>^er. 12 1 4. $3.35. Leipzig 

AUgemeine padoLgogische Rundschau. Popular- 
pddagogische Zeitschrift fur die Interessen 
des gesanimten Unterrichtswesens nacJi Innen 
und Aussen und dessen Vertrttung nach 
Aussen. 2414. With Supplement Blatter 
fur Haus und Schule. Ueberschaer. 24 | 4. 
$3.75. Berlin 

AUgemeine Schulzeitung fur das gesammte Un- 
terrichtswesen. Organ des Vereins fUr wis- 
senschaftliche Pddagogik. Stoy. 5214. $3.35. 
Jena 

American Journal of Education. Meewin. 
1214. $1.60. St. Louis 

The American Sunday • School Worker, For 
Parents and Teachers. Holmes. 12 | 8. $1.20. 
St. Louis 

Le Baccalaureat es Lettres, guide pratique du 
candidat. Pierre. 1218. $6.00. Paris 

Bulletin administratif du Ministere de Vln- 
struction puhlique. 1218. $4.00. Paris 

Bulletin de I'enseignement secondaire libre, 
public par la Socittt des chefs d'instituiion 
des dtpartements de la Seine-et-Oise et de 
la Seine-et-Marne. 1218. $1.75. Paris 

Bulletin officiel de Vinstruction primaire du 
dtp artement de la Seine. 1218. $2.50. Paris 

Tlie California Teacher. Devoted to the Educa- 
tional Interests of California. 1218. $2.00. 
Sacramento 

The Carolina Teacher. A Journal devoted to \ 
the Interests of Education in the State of 
South Carolina. Warren. 918. $0.75. 
Columbia 

The Common School and Iowa Journal of Edu- 
cation. 1214. $1.50. Davenport 

Cornelia. Zeitschrift fUr hdusliche Erziehung. 
PiLZ. 1018. $1.90. Leipzig 

Deutsche Blatter fUr erziehenden Unterricht. 
With Pddagogisches Anzeigeblatt. Mann. 
2418. $2.35. Langensalza 

VEcole primaire, reforme pedagogique. Quix. 
5214. $3.00. Paris 

El Educador Popular. 2414. $3.40. N.Y. 

L' Education. Journal des ecoles primaires. 
5218. $3.00. Paris 

L' Education chretienne. Journal des ecoles du 
Dimanche. 12 1 8. $1.25. Paris 

The Educational Journal of Virginia. Estill, 
Stevens, and Euffner. 1218. $1.50. Rich- 
mond 

The Educational Xews. A Weekly Record and 
Review. .5214. $2.25. London 

Educational Notes and Queries. A Medium of 
Intercommunication for Teachers. Henkle. 
1018. $1.00. Salem 



The Educational Times, and Journal of the 

College of Preceptors. 12 14. $3.00. London 

Die Erziehung der Gegenwart. Beitrdge zur 
Losung ihrer Aufgahe mit BerUcksichtigung 
von Fr. FroeheVs Grundsdtzen. Schrceter. 
1214. $1.70. Dresden 

Erziehungs-Bldtter. Amerikanische Schulzei- 
tung.) Fur Schule und Haus. Hailmann 
and Dcerflinger. 1214. $2.12. Milwaukee 

UEtude illustree. Journal dtdit aux fa- 
milies et aux institutrices. 5218. $4.00. 
Paris 

Evangelisch-Lutherisches Schulblatt. Monats- 
schrift fur Erziehung und Unterricht. LiN- 
DEMANN and Selle. 12 18. $2.00. St. Louis 

Freie pddagogische Blatter. Jessen. 5218. 
$4.20. Vienna 

Home and School. An illustrated Journal of 
Popular Education, Science and Literature. 
Davis. 1218. $1.50. Louisville 

The Illinois Schoolmaster. A Journal of Edu- 
cational Literature and News. Cook and 
Hewett. 1218. $1.50. Normal 

Indiana School Journal. Bell, Shortridge, 

and Brown. 12 | 8. $1.60. Indianapolis 
L' Instruction par V image. Texte par E.Vacca, 

dessins par J. Lhernault. 52 | 4. $3.75. 

Paris 
L' Instruction publique. Revue des lettres, 

sciences et arts. A. Blot. 24 j 4. $6.00. 

Paris 
Journal de l' Instruction Publique. 12 1 4. $1.00. 

Quebec . 
Journal des Insfituteurs et des Bibliotheques 

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Journal du Baccalaureat. J. Durandeait. 
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The Journal of Education. Devoted to Educa- 
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$1.00. Quebec 

The Journal of Education. 1214. $1.12. To- 
ronto 

The Journal of Education, in which are incor- 
porated the Educational Reporter and the 
Scholastic Advertiser: A Medium of Inter- 
communication for Teachers, Students, and 
others interested in Education. 1218. $3.00. 
London 

Kinder- Garten, Bewahr-Anstalt und Elem^n- 
tar-Klasse. Organ des deutscken Frobel-Ver- 
bandes. Kcehler, Schmidt, and Seldel. 
12 1 8. $1.70. Weimar 

Le Maitre d' etude. 5218. $4.00. Paris 

Manual general de V Instruction primaire, 
classe par ordre alphabetique. 52 1 8. $3.00. 
Paris 

The Maryland School Journal. Newell. 1018. 
$1.25. Baltimore 



Xl:. J^teigrer, 22 Sc. S-i Fraiakfbrt St., iWew Yorik. 



24 Education, General pftifotogy, Morfes of iicfcrmcc, etc. 



The Michigan Teacher. Ford. 1218. $1.60 
Kalamazoo 

Mona.tsschrift fur das gesammte deutsche Mad- 

chenschulwesen. Schmid. 12 | 8. $4.20. Thorn 
The National Sunday -School Teacher. Hazakd. 

1218 $1.50. Chicago 
National Teachers' Monthly. Mahony 1218. 

$1.00. N. Y. 
The Nebraska Teacher. Palmer. 12 | 8. $1.50. 

Beatrice 
Neue JahrhiXcher fur Philologie und Pdda^ogik. 

Fleckeisen and Masius. 1218. $12.50. 

Leipzig 
Netv England Journal of Education. (With a 

Kindergarten Department.) Bicknell. 5214. 

$3.00. Boston 
New York School Journal and Educational 

News. Kellogg. 5214. $2.00. N. Y. 
The North Carolina Journal of Education. 

Pool. 1218. $1.50. Kaleigh 
The Ohio Educational Monthly and National 

Teacher. Henkle. 1218. $1.50. Salem 
Pddagogisches Archiv. Centralorgan fur Er- 

ziehung und Unterricht in Gymnasien, Real- 

schulen und hoheren BUrgerschulen. Krumme. 

10 1 8. $6.70. Stettin 
The Pennsylvania School Journal, devoted to 

School and Home Education. Wickersham. 

1218. $1.60. Lancaster 
Der praktische Schulmann. Archiv fur Mate- 

rialien zwn Unterricht in der Real-, BUrger- 

und Volksschule. Richter. 818. $4.20. 

Leipzig 
Recueil des Lois et Actes de V Instruction pu- 

blique. \S. $3.00. Paris 
Revue de V Enseignement Chretien. 12 j 8. $7.50. 

Paris 



Rheinische Blatter fUr Erziehung und Unter- 
Hcht. [Founded in 1827 hy A. Diesterweg.) 
Lange. 618. $3.35. Frankfort 

Schermerhorn's Monthly. A Magazine for 
Parents and Teachers. 1218. $2.00. N, Y. 

The Scholastic Register. A Monthly Paper de- 
voted to the Interests of the Scholastic Pro- 
fession. 12 1 4. $1 00. London 

The School Board Chronicle. An Educational 
Record a7id Review. 5214. $6.50. London 

TJie School Bulletin and New York State Edu- 
cational Journal. 12 1 4. $1.00. Syracuse 

The Schoolmaster. An Educational Newspaper 
and Review. 52 1 4. $2.25. London 

The Sunday-School Journal for Teachers and 
Young People. Vincent and Freeman. 
1218. $0.65. N. Y. 

The Sunday-School Times. Trumbull and 
Peltz. 5214. $2.15. Phila. 

Die Volksschule. Eine pddagogische Monats- 
schrift. Hartmann. 1218. $2.00. Stuttgart 

The Western. A Journal of Literature, Edu- 
cation, and Art. Morgan. 12 j 8. $2.00. 
St. Louis 

West Virginia Educational Monthly. Blair 
and GriBBENS. 1218. $1.60. Parkersburg 

Wisconsin Journal of Education. Searing 
andPRADT. 1218. $1.10. Madison. 

Zeitschrift deutscher Zeichenlehrer. Hertzeb 

2414. $3.35. Berlin 
Zeitschrift fur das Gymnasialwesen. Hersch- 

FELDER, HOFMANN, and RUEHLE. 12 1 8. 

$7.50. Berlin 
Zeitung fur das hohere Unterrichtswesen 
Deutschland's. Weiske. 52 j 4. $3.35. Leipzig 



NOTE. 

The Periodicals enumerated in this Catalogue may all be ordered from E. Steiger. 

The prices quoted are based upon the latest information at command. They are, 
however, liable to vary; are, consequently, open to reduction or increase without pre- 
vious special notice, and are pavable in advance when the order is given. —The figures 
placed next before the perpendicular stroke (1) denote the number of issues of tha 
Periodicals per year thus: 12] = monthly ; 52| = weekly, etc.). The figures next after 
this perpendicular stroke mean the size, thus : |4 = quarto; 18 = octavo; 1 12 = duo. 

decimo, etc. 

The names in small Caps, added to the titles of most German and French Period- 
icals, are those of the Editors. 



E. Steiser, 33 & ^24 J^vsn^Vatavt St., lN"ew York, 



May, 1876. 



im.4>%wK^wt%m> #ifte 



AND 



Occupation IVIaterial 



Note. This Revised Price-List cancels previous Catalogues. 



ihj Jirst 6ift. 




For the youngest children: 
Six soft Balls of various colors. 

Aim: to teach color (primary — red, blue, yel- 
low — and secondary or mixed — green, violet, 
orange) and direction (forward and backward, 
right and left, up and down); to train the eye; 
to exercise the hands, arms, and feet in various 
plays. 

A Set, in Wooden Box, with Directions 

{FroebeVs First Gift for Babies\ $1.00 

Extra Sets, of 6 Balls, $0.60 

Directions for the use of the First Gift may 

also be found in 
Hoffmann, Kindergarten Toys and how to use 

them. A Practical Explanation of the first ^ix 

Gifts of FrobeVs Kindergarten, $0.20 

and in many other publications. 



WU ^moM (iifl. 



Sphere^ Cube, and Cylinder. 

Aim: to teach form, to direct the attention 
of the child to similarity and dissimilarity 
between objects. This is done by poioting 
out, explaining, and counting the sides, corn- 
ers and edges of the cube; by showing that 
y^ fm II the properties of the sphere, cylinder, and cube 

\ ^ ^1 /m ^^® different on account of their difference of 

N^^ ^P ^P shape; by pointing out that the apparent form 

of the sphere is unchanged, from v/herever 
viewed, but that the apparent forms of the 
cube and cylinder differ according to the point 
from which they are viewed. 
The forms are of wood, machine-made for 
this special purpose; are neat and provided with the necessary staples and 
holes for hanging. 

In Wooden Box, with cross-beam for hanging the forms, $0.70 

For Directions see Hoffmann, Kindergaiien Toys, and other publications. 

E. Stei8:er, SQ 6c S4 Fraixlifort St.. Tiew York. 




kindergarten ®ift8 and ®ccupatton Materiaf. 







Large Cube, diyided into eight small cubes of equal 
size. Aim: to illustrate form and number; also to give 
the first idea of fractions. 
In Wooden Box, $0.30 

Diagrams and Directions for using the Third Gift. 
In Wrapper, $0.30 

See also Hoffmann, Kindergarten Toys, 

and other publications. 




WiW% ^nmi> BuiWittg ^u. 

Large Cube, divided into eight oblong blocks. — The points of 
similarity* and difference between this and the Third Gift should be indicated. 
In Wooden Box, $0.30 




Diagrams and Directions for using the 

. Fourth Gift. In Wrapper, $0.30 

See also Hoffmann, Kindergarten Toys, etc. 



E. JSteig-er, SS &c 24 I^raiTLlcfbi-t St., IVe^vr Yorlt, 



kindergarten Sifts and fficcupation Jllatmal. 



mt Jifth (iifi 



WiUi% l^Uvi Building Ba3e. 



This is a continuation of, and complement to, the Third Gift. It con- 
sists of twenty-one whoUf six half-, and twelve guar/er-cubes, forming alto- 
gether one large Cube. 




Illlll 




M 







In Wooden Box, $0 75 

Diagrams and Directions for using the Fifth Gift. In Wrapper, $0.60 
See also Hoffmann, Kindergarten Toys, etc. 



mt Jiffh (iift B. 



The Fifth JBiiilding Sox (a combination of the Fifth and Second 

Gifts). In Wooden Box, $1.00 

Diagrams and Directions for using the Fifth Gift B. In Wrapper, $0.50 

©he mtti mft 

This is a continuation of, and complement 
to, the Fourth Gift. It consists of eighteen 
whole oblong blocks, three similar blocks 
divided lengthwise, and six divided breadth- 
wise, forming altogether one large Cube. 

In Wooden Box, $0. 75 

Diagrams and Directions for using the 
Sixth Gift. In Wrapper, $0.60 

See also Hoffmann, Kindergarten Toys, etc. 

The Fifth Gift (Fecebel's Third Building Box), extra -large size, 
11 cubic feet. In strong Wooden Box, $7.20 

The Sixth Gift (Fkgebel's Fourth Building Box), extra-large size, 
li cubic feet. In strong Wooden Box, $9.00 

JE. J^teig^er, 22 &^ Q^r Fraixkibrt St., ilVe^^ Yorfe. 




kindergarten ®ifts and Occupation Material. 



ih« ^mnili (iift. 



Quadrangular and triangular Tablets 

of polished wood. These tablets, as well as the previous Gifts, are 
designed for instruction in reversing the position of forms and com- 
bining them. In the six previous Gifts the child had to do with solids: 
by the tablets the plane surfaces are represented; these are followed by 
the straight line in the Eighth Gift, and the curve in the Ninth Gift. 






A, Four large right-angled Triangles. 
In Wooden Box, $0. 25 



B. Eight squares. In Wooden Box, $0.30 
Diagrams to same. In Wrapper, $0.40 



0. Nine large equilateral Triangles. In 

Wooden Box, $0.30 

Diagrams to same. In Wrapper, 

$0.40 

, Sixteen isosceles Triangles. In Wooden 

Box, $0.30 

Diagram.s to same. In Wrapper, $0.40 



E. 



Thirty-two isosceles Triangles. In Wooden Box, 

$0.40 
Diagram.s to same. In Wrapper, $0.40 

F. Fifty -four equilateral Triangles. In 

Wooden Box, $0.50 

Diagramis to same. In Wrapper, $0.40 

G-. Fifty-four isosceles Triangles. In Wooden Box, 

$0.50 
Diagrams to same. In Wrapper, $0.40 





iililil^ 



H. Fifty-six 
scalene Tri- 
angles. In Wooden 
Box, $0.60 

Diagrams to same. 
In Wrapper, $0.40 




E. Stelager, SS Sc S4r J^^raIll^:^ort St., 3Ve^w ^Sfort. 



kindergarten ®ifts and ©ccupation Maimal, 




I, Sixty-four obtiise^angled Triangles. 

In Wooden Box, $0. 60 

Diagrams to same. In Wrapper, $0.40 

Box containing, in five divisions. Squares and the 
four diiferent kinds of Triangles (of binder's board), 
with Diagrams, ^ $1.60 

Box with glass cover, containing, in five divisions. 
Squares and the four different kinds of Triangles, 
in finely colored and polished wood, $6.00 




mi (Biglith (iift 



Sticks for Stick -laying. This 
Gift consists of thin wooden Sticks, 
about 13 inches long, to be cut into 
various lengths by the teacher or 
pupil, as occasion may require. 
These Sticks, like most of the pre- 
vious Gifts, are designed to teach 
numerical proportions and forms. 
Stick-laying is an excellent prepara- 
tion for drawing. The Multiplica- 
tion Table is practically taught by 
means of this Gilt. Reading, ac- 
cording to the phonetic method, is 
taught by imitating with these 
Sticks the letters of the Alphabet. 
In the same way the Eoman and 
Arabic numerals are taught previous 
to instruction in writing. 

Package of 1000 Sticks, 1 inch 
^ong, $0.30 

Package of 1000 Sticks, 2 inches 
^ong, $0.30 

Package of 1000 Sticks, 3 inches 
^ong, $0.30 

Package of 1000 Sticks, 4 inches 
long, $0.30 

Package of 1000 Sticks, 5 inches 
^ong, $0.30 

Package of 500 Sticks, 13 inches 

^ong, $0.50 

Diagrams, in Wrapper, $0.30 

Box with Sticks 1, 2, 3, 4, and 5 
inches long, $0.35 



n U \/ D 

OPQR 
PAPA 




7 7 

IVV 



Frohd's Kindergarten Occupations for the Family. No. 1. Stick-laying, $0.75 
E, Steisrei^, ss ^ ^^ Fra»l^oi-t Bt„ IS^ew York, 



kindergarten ffiifts and Occupation itlatcriat. 




©he finth (gift. 




Rings for Hitig-laying, This 
Gilt consists of whole and half Bings 
of various sizes, in wire, for forming 
figures. These Eings, like the Sticks 
in the Eighth Gift, are intended to 
teach the first elements of form as 
an introduction to drawing. 

Box of whole and half Eings of 
various sizes, $0. 75 

Diagrams, in Wrapper, $0.60 

ma Ifinth €ift. 

Drawing on Slates 
and Paper. The 

material used is, first, 

Slates grooved in 

squares, next. Paper 

ruled in squares. This 

method of beginning 

drawing is the most 

systematic and per- 
fect ever invented for 

young children. It is 

interesting to note 

how rapidly, by it, 

even the youngest pu- 
pils advance. 
Slates, 13J by 10 inches 

(No. 12), grooved in 

squares, 4 inch wide, on 

one side, each $0.50 
Slates, 12 by 9 inches 

(No. 9), grooved in 

squares, each $0.40 

Slates, 10 by 7J inches 

(No. 6), grooved in 

squares, each $0.30 

Slates, 8 J by 6 J inches 

(No. 4), grooved in 

squares on one side, with 

narrow frame, rounded 

corners, each $0.30 

Slate pencils (fine), per 

doE., $0.15, per gross, 
$1.50 
Diagrams, in Wrap- 
per, $0.30 




:ES, (Stelsr^x*, 22 6c, S4= FraiUcfort St., I^e^w Yorlc, 



ilindergartm ©ifts and fficcupation iHatmaf. 



Drawing-Books, ruled in squares, 4 inch wide, on both sides, each book 
containing 12 leaves, per doz., $0.70 

Drawing-Books, ruled in squares, one-sixth inch wide, on both sides, 
per doz., $0.70 

Paper ruled in squares, i inch wide, on both sides, per quire (24 sheets), 
each 14 by 17 inches, $0.40 

Paper ruled in squares, one-sixth inch wide, on both sides, per quire, $0. 40 

Pencils, per doz., $0.75 

Pencils (fine), per doz., $0.90 

K. Fbcebel's Elements of Designing, on the Developing System, f(yr Elemen- 
tary School Classes, and for Families, 4 Parts, each containing 24 pages ruled 
in squares, with designs and space for copying, each part $0.35 

Part I. Straight Lines, and their Combinations. 

Part n. Straight Lines, and their Combinations. 

Part in. Straight Lines, and their Combinations. 

Part IV. Circles and Curved Lines, and their Combinations. 

Each page of the given examples is followed by a blank page for the Composi- 
tions, Combinations, or Inventions of the pupil. 

M'oebeVs Kindergarten Occupations for the Family. No. 2. Drawing. $0.75 

iBU (KlflMnth (Sift. 

Perforating {Pricking) Taper. 




A Package of 50 leaves of paper, 11 by 85 in- 
ches, ruled in squares on one side only, $0.50 
Package of same, 25 leaves, $0.30 




Perforating-Needles with long handles, 

per doz., $0.60 

Perforating-Needles with short handles, 

per doz., $0.60 

Perforating-Needles with long black handles, 

per doz., $0.25 

Perforating-Cushions, 

Diagrams, in Wrapper 




each $0.25, per dozen, $2.40 
$0.30 



FroebeVs Kindergarten Occupati(ms far the Family. No. 3. Perforating. $0-75 



i^indcrgartcn €S!fls and Occupation Jllatcriat. 



m^ iujfiifth €ift. 



Embroidering, The Perforating Material is also used in this Gift: 
after the pattern is perforated, it is embroidered with colored silk or 
worsted on card-board. 



X 




X 




X 




X 




X 




X 






















u 


, 


X 


1 


X 




X 




X 




X 





Material for perforating and em- 
broidering, in Wrapper, Nos. 1, 2, 
3, 4, each $0.50 

Card-board ruled in squares on 
one side, Package of 25 leaves, 

$0.25 

Blotting Pad, Package of 25, 

$0.15 

Card -board (fine), Package 
of 25, $0.20 

Twelve Designs, 8 by 6 inches, 
for perforating and embroidering, 
in Wrapper, Nos. 1 to 12, each 

$0.50 

Card-board (fine), 8 by 6 inches,, 
to be used with these Designs, 
Package of 12, $0.20 

Twelve Designs, 5i by 4 inches, 
for perforating and embroidering, 
in Wrapper, Nos. 1 to 6, each 

$0.35 

Card-board (fine), 5i by 4 in- 
ches, to be used with these De- 
signs. Package of 12, $0.10 

Card-board in sheets, 22 by 27 
inches, in various colors, per 
sheet $0.10 or $0-12 

Baskets for Cards or Needle- 
work, embossed, for perforating 
and embroidering in worsted or 
silk, and otherwise ornamenting 
and making up, 3 sizes, Y, 8, and 
9 inches wide respectively. Pack- 
age of 6, assorted, $0.50 

Worsted Needles, per doz., in 
Wrapper, $0.15 

Worsted, 1 2 assorted colors, with 
3 Worsted Needles, in Wrapper, 

$0.25 
Embroidering Silk, 12 assorted colors, with 3 Needles 





/f^vk.^ 


mMi 


v^ 


^^S 


\\ 


// \\]// 


J^^l /^^ 


L-^ 


^s^^-n^^ 




in Wrapper, $0.35 



E. {Steigrei?, 2i3 & S-4 ITranlifbi-t St., NeT¥- York. 



kindergarten ©ifts and ®ccupation illafcriaL 



9 



^\u Mxixtmih (Sift. 




Cutting 'Paper. Squares 
or Triangles of Paper are 
folded, cut according to 
certain rules, and formed 
into figures. The child's 
inclination for using the 
scissors is here so inge- 
niously turned to account 
as to produce very grati- 
fying results. 

Package of 100 squares, 
white, $0.20 

Package of 100 squares 
colored, $0.20 

Package of 100 squares, white and colored, mixed, 
Diagrams to same, 




Scissors, for Paper-Cutting, with rounded blades, 



$0.20 

$0 75 

per pair $0.40 

per doz. $4.00 

Package of 30 leaves, 9 inches square, of stout, ultramarine paper, for 

mounting the cut figures, $0. 50 

Package of 30 leaves, 9 inches square, of Manilla paper, $0.30 



ihe Jourtfifinth €ift. 



HI 



:ill!illiiIllllliKllilliliili!lll!!l!ill 

aiiilillilliimi!llii!iil!lll!liill!l!!lliilll!llllllHIHI!l!! 
;liliiIliiiElillllHll9l!liilliilllillitl!iil!llll!ill!ii™ii!illii'lilii 
ilB'llil!Hlfilllili!llll!!llliil!!iS!iiIill'Jiillilliillilii"l''ii 
llllililiffllli!iOiil!liiaUi!!!l!liili|!ll!l!!lli!!|!lMl 
llii!ffliii!ill!ii!!!li!!llll9llli!llilillii''J«l!!ilij!llll!liillllll!f 
!lll!]!!!!Hliri!!llli'J!W,llll:t!!lillllilliiliillllillllllll!llill 
|ilil!!!lilll!l!iiDlll!iaiilllllllllllllllil!illl!i!i!i:ililiil!i!lllilllli 
.JiSiinii|l!ilillClH!iiifJHiill!llillliill!!ii!!ili!lll!irililMllili!ii' 
I llllll!i!iii!l!illl!iiilli!lllllilll!lilillPi!!!llliRI!ailllllll!lll 
iililiiyi;::l;|liiiilli;ill!l!l!!:;i!i;!!lllll^iIiil!!ii!in!lill!ISillllll! 




Weaving Paper. Strips of col- 
ored paper are, by means of a steel, 
brass, or wooden needle of peculiar 
construction, woven into another 
(differently colored) leaf of paper, 
which is cut into strips throughout 
its entire surface, except that a mar- 
gin is left at each end to keep the 
strips in their places. A very great 
variety of desip^ns is thus produced, 
and the inventive powers of teacher 
and pupil are constantly stimulated. 




:e:. ."Steigei-, S2 ifc 24. I^rai^lifbrt St,, 'SS^er^ Yorfi. 



10 



i^indergoden ®ift8 and fficcupation llllateriaL 



Mats, 7 by 6 inches, with 
slits and corresponding 
strips for weaving, slits 
i inch wide (No. 1), 
Package of 1 doz., of 
various colors, $0. 20 

Mats, 7 inches square, slits 

i inch wide (No. 11), 

'Package of 1 doz. $0.20 

Mats, 7 by 6 inches, slits 
i inch wdde (No. 2), 
Package of 1 doz., $0.20 

Mats, 7 inches square, slits 
i inch wide (No. 12), 
Package of 1 doz., $0.20 

Mats, 7 by 6 inches, slits 
1-3 inch wide (No. 3), 
Packageof Idoz., $0.20 

Mats, 7 inches square, slits 
1-3 inch wide (No. 13), 
Package of 1 doz. $0. 20 

Mats, 7 by 6 inches, slits 
1-6 inch wide (No. 4), 
Package of 1 doz., $0.20 



Mats, 7 inches square, slits 1-6 inch wide 

(No. 14), Package of 1 doz , $0.20 
Mats, 7 by 6 inches, slits 1-8 inch wide 

(No. 5), Package of 1 doz., $0.20 
Mats, 7 inches square, slits 1-8 inch wide 

(No. 15), Package of 1 doz., $0.20 
Mats, 7 by 6 inches, slits 1-12 inch wide 

(No. 6), Package of 1 doz., $0.20 




E:. Steis^r, QS 4fc J3-4. ITraiiltfbrt St., JS€>^w York. 



kindergarten ®ifts and Occupation Jllatertal. 



11 



Mats, 7 inches square, with alternate wide and nar- 
row slits and corresponding strips (No. 16), Package 
of 1 doz., $0.20 

Mats, like the foregoing — No. 16 — bine and white 
paper only (No. 17), Package of 1 doz., $0.20 

Mats, 7 by 6 inches, with alternate wide and nar- 
row slits and corresponding strips (No. 21), Package 
of 1 doz., $0.20 

Mats, 7 by 6 inches, in which one wide slit alternates 
with two narrow ones, with corresponding strips 
(No. 22), Package of 1 doz., $0.20 

Mats, 7 by 6 inches, in which one wide slit alternates 

with three narrow ones, with corresponding strips 

(No. 26), Package of 1 doz., $0.20 

(Note. Mats will be cut to order in quantities not less 
than 12 doz. of a particular kind.) 

Diagrams, in Wrapper, $0.30 

Wi'appers to protect the mats from creasing when 
left unfinished in the Kindergarten or at home, 
per doz., $0.60 



Weaving-Needles of wood, long, per dozen, $0.50 
Weaving-Needles of wood, short, per doz., $0.30 

Weaving-Needles of steel, per doz., $1.20 

Weaving-Needles of brass, per doz., $1.20 

Material for book-marks, strips 1-8 inch wide, per 

Package, $0.20 

Material for book-marks, strips 1-4 inch wide, per 

Package, $0.10 

Material for book-marks, strips 3-8 inch wide, per Package, 

FraebeCs Kindergarten Occupations for the Family, No. 4. Weaving. 




mn Jiftwnth (Sift. 



Plaiting. Fifty Slats, 10 inches long and i inch 

wide, for interlacing, to form geometrical and 

fancy figures, $0.35 

Diagrams to same, $0.75 




mt ^MmW (iift. 



A Set of Jointed Slats with 9 links. 

per Set, $0.20 

Diagrams to same, $0.30 



E, Steigrer, SS &o S4 Franlirort St., T^ew Yoz^lx^ 




12 



ilindetgartcn ®ifts and 6^ccupation Jllatmat. 



ih« ^ficcntwnth dift. 





Paper Strips of various 
colors, lengths, and 
widths, folded length- 
wise, are used to re- 
present a variety of geo- 
metrical as well as fancy forms, by plaiting them according to certain mles. 
Packages of Paper Strips of different length and width, containing 
100 each, $0.20 

Diagrams to same, $0.75 




ihe iishlfienth (Sift, 



Folding Paper. The material for Paper- 
Folding consists of square, rectangular, and 
triangular pieces, with which variously 
shaped objects are formed, and the elements 
of geometry are taught in a practical man- 
ner. The variety is endless and prepares 
the pupil for many useful similar manual J^ 
performances in practical life. 

100 leaves, white, 4 inches square, 80 20 

100 leaves, colored, Si inches square, $0.20 

100 leaves, colored, 4 by 2 inches, $0.15 

100 equilateral Triangles, white, sides 

6 inches long, $0.30 

100 equilateral Triangles, colored, sides 

4 inches long, $0.25 

Diagrams to same, $0.75 




mt MmiuwWx (iift. 



Peas or Cork Worh, Peas are soaked in water 
for six or eight hours, and pieces of wire, of various 
lengths, pointed at the ends, are stuck into them 
for the purpose of imitating real objects and the 
various geometrical figures. Skeletons are thus pro- 
duced, which develop the eye for perspective draw- 
ing most successfully. Sticks belonging to the 
Eighth Gift are also used for this purpose. 

In place of Peas many persons prefer to use small Cork Cubes. 

Wires of different lengths, per Package, 

Cork Cubes, per Package of 100, 
Diagrams to same. 




SO 20 
$0.25 
$0.75 



kindergarten ^ifts and Occupation JUatctiat. 1^ 

^hi WmnMh dUft. 

M^odeling» Bees-wax, Clay, Putty or other material, worked with a 
small wooden knife, on a light smooth board, is used for the purpose. 
These materials can be bought almost everywhere. 

Modeling-Knives, of wood, larger and better kind, each $0. 20 

Modeling-Boards of wood, each $0. 12 

Diagrams to same, $0.76 



4®=- Customers will please bear in mind that the method of describing Kinder- 
garten Gifts, &c., in this Catalogue, is that adopted in America, which differs consider- 
ably from the one used in Grermany and England. It is very important to remember 
this when ordering the Gifts &c. Only the first six Gifts are used in a strictly serial 
order, the Planes, Sticks, Weaving, and Embroidering materials being introduced at 
the same time as the Third Gift, so that the work of no two or three consecutive days 
need be alike. — The designation by numbers (No.) of various articles is entirely 
arbitrary, and is done solely for the purpose of enabling customers to order the exact 
kinds they desire to receive. — Bequests to take back or exchange goods sent in con- 
formity with orders must be declined. 



Kindergarten Tables ^ 22 inches high, with cover of bass-wood (white- 
wood), marked off in squares one inch wide, nicely finished and 
varnished, 

Tables, 30 inches wide, 6 feet long, $7-50 

Tables, 30 inches wide, 9 feet long, $10-00 

Tables for one child, each, 20 inches wide, 30 inches long, $3.00 

Oil-'Cloth Covering 9 with light colored ground, one yard wide, marked 
off in squares one inch wide, supplied to order at $0.50 per running foot. 
(This kind of covering may be used to fit ordinary tables tempora- 
rily for Kindergarten purposes. ) 

Kindergarten Chair s^ per dozen from $13.50 to $18.00 

[Boxing and Shipping Expenses will be charged extra.] 



6ust of Friedricli Frcebel, 8 inches high, with Console^ $4.00 

Photograph of Friedricli FrcBbel, after a relief by O. Metee, 8 by 9 
inches, $3.00 



The List on the foregoing pages comprises only part of my Stock 
of Kindergarten Gifts, Occupation Material, etc. 

A very large assortment of kindred articles is on hand, and additions 
are incessantly made, both by importation from Europe and by domestic 
manufacture, so as to render mine the most complete and m.ost ex- 
tensive Repository of the kind in America. 

To meet the growing demand, I offer, at a concession from regular 
prices. Selections — more or less complete— of Kindergarten €Hfts 



14^ kindergarten ffiifts and ®ccupaiion Material. 

and Occupation M^aterialf sttfficieiit for a smaller number of children. 
As such I offer the following: 

STEIGER'S 
liliixdLerg'ax'ten Ohest IVo. 1. 

A Selection of Kindergarten Gifts and Occupation Material, suitable for 
use in Families. In Wooden Box. Price $12.00. 

Contents; 

FnisT Gift. 

Second Gift. 

Thtrd Gift with Diagrams, 

Foueth Gift with Diagram 

Fifth Gift with Diagrams. 

Sixth Gift with Diagrams. 

Seventh Gift: 3 boxes of triangular tablets (G.H.I.) with Diagrams to each. 

Eighth Gift with Diagrams. 

Ninth Gift with Diagrams. 

1 Slate (No. 9) and 6 Pencils, with Diagrams. 

2 Dozen Designs (large and small) for Perforating and Embroidering, 

2 Packages of Card-board and 2 Perforating-Needles. 

1 Package of Paper for Cutting and Folding. 

2 Packages of Weaving-Mats and Strips, and 6 Weaving-Needles (of wood) 

and Diagrams. 

1 Package of Slats for Interlacing, with Diagrams. 

Corks and Wires, 1 Package of each, with Diagrams. 

1 Modeling-Knife. 

1 A. Douai. The Kindergarten. With 16 Plates and Songs. Cloth. 

1 Hofimann. Kindergarten Toys and how to use them. A Practical Explana- 
tion of the first six Gifts. 

STEIGER'S 

A smaller Selection of Kindergarten Gifts and Occupation Material, 
suitable for use in Families. In Wooden Box. Price $8.00 

Contents: 

Fifth Gift JB (a combinatioi) of the Second and Fifth Gifts), with Diagrams. 
Eighth Gift with Diagrams. 
Ninth Gift with Diagrams. 

1 Slate (No. 9), 6 Pencils, and Diagrams. 

2 Dozen Designs (large and small) for Perforating and Embroidering, 

2 Packages Card-board, and 2 Perforating-Needles. 
1 Package of Paper for Cutting and Folding. 
6 Packages of Weaving-Mats and Strips, with 6 Weaving-Needles (of wood), 

and Diagrams. 
1 Package of Cork Cubes, and 1 Package of Wires, with Diagrams. 
1 A. Douai. 7he Kindergarten. With 16 Plates and Songs. Cloth. 

Note. No request for a departure from these selections can be entertained, when the 
reduced price for the whole is claimed. 



JES. iSteis:e^9 SS Sc S4 FrarLkfort St., JN"eTr York, 



E. Steiger's Catalogues 

entunerated hereafter are intended, on the one hand, to keep the public in- 
formed of what he has in stock in the various departments of literature ; of 
books, therefore, which are nsnally on hand, and can be at once supplied. On 
the other hand, these Catalogues serve as a guide to the best publications in 
their special branches of literature, and such as are most serviceable in this 
country. These Catalogues having now reached a considerable number, and 
being continually made more comprehensive by additions and revisions, they 
can, for the future, as a rule, be sent only on receipt of the subjoined nominal 
prices which simply cover in part the expenses of production and the prepay- 
ment of postage. 



No. 1) Steiger's Festival Catalogue. A List 
of German Books and Fine Illustrated 
Works more especially adapted for pres- 
ents. (Classics, Romances, Novels, Tales, 
Poems, Anthologies, Dramatic Works, 
Fine Editions with illustrations and the 
choicest productions in the Departments 
of History, Geography, Natural Sciences, 
Philosophy, Aesthetics, Pedagogy,History 
of Literature and the Art of Poetry, Ma- 
Bic- and Art-Literature, Protestant The- 
ology, Encyclopaedias and Dictionaries, 
Commercial Science, Works for the higher 
culture of the female sex,Books on House- 
keeping, Cookery, and Domestic Economy, 
Humorous Literature, etc.) 240 pages. 

(15 Cents.) 

la) Steiger's Festival Catalogue. First Divi- 
sion. (Classics, Romances, Novels, etc.. 
Poems, Anthologies, Dramatic Works,— 
the latest Juveniles, and Kindergarten 
Literature.) 72 pages. (5 Cents.) 

2) Library of Fiction. A Catalogue of select 
Romances, Novels, and Tales by German 
authors, and the better class of similar 
Foreign Works in German translations. 

^ Cents.) 

3) Steiger's Catalogue of G-erman Picture- 
Books and Juveniles. Classified accord- 
ing to the age of children. (4 Cents.) 

4) Steiger's Theological Library. A System- 
atized Catalogue of German Publications 
in the Department of Protestant Theology, 

(5 Cents.) 

5) Steiger's Philosophical Library. A Sys- 
tematized Catalogue of German Publica- 
tions in the Departments of Philosophy and 
Esthetics. (4 Cents.) 

6) Steiger's Pedagogical Library. Part I. 
A Systematized Catalogue of German Pub- 
lications on the Theory of Education and 
Instruction. (4 Cents.) 

7) All Illustrated Catalogue of Kindergarten 
Gifts and Occupation Material, together 
with a List of Kindergarten Literature, in 
German, English, and French. (Gratis. 

8) Steiger's Descriptive School-Book Cata 
logue. A List of Educational Publications 
With Notes, Specimen pages, Reviews, etc, 

(Gratis. 



9) Steiger's Bibliotheca G-lottica. Part L 
A Catalogue of Dictionaries, Grammars, 
Readers, Expositors, etc., of mostly Modern 
Languages spoken in all parts of the Earth, 
except English, French, German, and 
Spanish. First Division : Abenaki to 
Hebrew. (5 Cents.) 

10) Steiger's Bibliotheca Glottica. Part II. 
A Catalogue of Dictionaries, Grammars, 
Readers, Expositors, etc., of the English Lan- 
guage, in English, Czech, Danish, Dutch, 
French, German, Italian, Polish, Portu- 
guese, Russian, Spanish, Swedish, and 
Turkish. (3 Cents.) 

11) Steiger's Bibliotheca G-lottica. Part III. 
A Systematized Catalogue of Publications 
on the German Language and Literature, 

(5 Cents.) 

12) G-erman Dialects. A Catalogue of more 
than 500 Publications, representing all 
the Dialects spoken in the German Em- 
pire and neighboring German-speaking 
countries. Together with Maps, Descrip- 
tions of land and people, and Guide-Books of 
Germany. (Gratis.) 

13) Steiger's Scientific Library. Part I. A 
Systematized Catalogue of German Books 
and Periodicals in the Departments of 
Natural Sciences, Mathematics, Astronomy, 
Military and Commercial Science. (5 Cents.) 

14) Steiger's Medical Library. A System- 
atized Catalogue of German Books and 
Periodicals in the Departments of Medi- 
cine, Pharmacy, and Veterinary Science. 
With Index. (6 Cents.) 

15) Steiger's Library of Chemistry and Phar- 
macy. Part I. A Catalogue of German 
Books and Periodicals in the Departments 
of Chemistry and Pharmacy. With Index, 

(3 Cents.) 

16) Steiger's Technological Library. Ger- 
man Books and Periodicals in the Depart- 
ment of Tec/moZop'?/. With Index. (4 Cents.) 

17^ Steiger's Library of Engineering. (Ger- 
man Books and Periodicals in the Depart- 
ments of Engineering, Mechanics, Archi- 
tecture, Mining, etc. With Index. (4 Cents.) 



EL Stelsrer, SS & 24 Fraxikfort St., JSg^^ Yoirlk:. 



18) Steiger's Library of Architecture. Parti. 
A Catalogue of German Publications in 
the various Departments of Architecture, 
Handicraft, Workmanship, and other cog- 
nate branches. To which are added Lists 
of Contents, Descriptive Notices, and Re- 
views. With Index of Subject-Matters of 
all Publications enumerated, German- 
English and English-German. With Ad- 
ditions. (6 Cents.) 

18a) A short List of American and British 
Publications on Architecture, Art, Orna- 
mentation, etc., together with a List of 
American, British, and French Periodicals 
in the Departments of Architecture, Art, 
Engineering, Technology, etc. (Gratis.) 

19) Steiger's Farmers' Library. A System- 
atized Catalogue of German Books and 
Periodicals in the Departments of Agri- 
culture, Horticulture, Domestic Economy, 
Forestry, Sports, etc. (4 Cents.) 

20) Steiger's Historico - Geographical Li- 
brary. A Catalogue of German Books and 
Periodicals in the Departments of His- 
tory, Geography, and allied Sciences. With 
Index. (6 Cents.) 

21) Steiger's Law Library. Part I. German 
Books and Periodicals in the Departments 
of Jurisprudence, Politics, Statistics, etc. 
With Index. (5 Cents.) 

22) Art and Music. A Systematized Cata- 
logue of the best German Books and Peri- 
odicals on Art, Music, etc. (3 Cents.) 

23) Steiger's Library of G-ymnastics. A Sys- 
tematized Catalogue of German Publica- 
tions on the several kinds of Gymnastics ; 
together with a List of Song and Glee 
Books. , (Gratis.) 

24) Steiger's Theatrical Catalogue. A Cata- 
logue of the best Plays in the German 
Language, selected from the dramatic 
Literature of Germany, France, England, 
Spain, etc. [About 2,600 pieces.] (5 Cents.) 

25) Steigers Literarische Berichte. A Bulle- 
tin of new German Publications. [Issued 
since 1873, partly as a continuation of 
Steiger's Literarischer Monatsbericht.) 

(Nos. 1 to 78, 25 Cents.) 

26) Catalogue of E. Steiger's German Cir- 
culating Library. With Additions. (5Cts.) 



27) Steiger's Catalogue of Periodicals. A 
Systematized enumeration of the Period' 
ical Publications of German Literature. 
With an Appendix: Works isiuedin Parts. 

(5 Cents.) 

31) Steiger's Illustrated Descriptive Cata- 
logue of Globes, Atlases, and Maps, Kinder- 
garten Gifts and Occupation Material, and 
Educational Publications. 8vo. (Gratis.) 

32) Steiger's Pedagogical Library. Part n. 
Education, General Philology, Works of 
Reference, Handbooks for Teachers, etc. 
A Descriptive Catalogue of American, 
British, German, French, and other Books 
and Periodicals (exclusive of School- 
Books). (Gratis.) 

38) The Periodical Literature of the United 
States of America. With Index and Ap- 
pendices. By E. Steiger. 8vo. Cloth, $1.00 

[This Catalogue enumerates about 8,300 
Periodical Publications, and the Index of 
Subject-Matters is given in English, Ger- 
man, DutchjFrench, Italian, and Spanish.] 

39) Steiger's Classified Catalogue of Amer- 
ican, British,German, and French Period- 
icals, in the Departments of Medical Sci' 
ences. Chemistry, and Pharmacy — Natural 
Sciences — Architecture, Engineering, Math- 
ematics, etc. — Technology, Commerce, Finance, 
etc. — Agriculture, Domestic Economy, Arts, 
Spo7'ts, Fashions, etc. [This is a List of 
about 1,200 of the best Periodicals in the 
above-named Special Departments.] 8vo. 

(Gratis.) 

40) Steiger's Descriptive Catalogue of Scien- 
tific, Technological, and other Special 
Periodicals published in the United States 
of America. With Index of Subject-Mat- 
ters in English, German, and French. 8vo. 

(Gratis.) 

41) Specimen of an Attempt at a Catalogue 
of Original American Books. With Index 
of Subject-Matters. By E. Steiger. 8vo. 

(Gratis.) 

Guide through E. Steiger's Stock o*" German 

Books. An alphabetical Index of about 800 

Departments and Specialties of which 

works are on hand. German and English. 

(Gratis.) 



An elegant Patent Self -Binder, large enougli to hold the majority of the 
ofeove-named Catalogues (most of which are in 12mo), maybe had for $1.00. 

Other Lists of Books are in preparation. 

Catalogues of Second-hand Books in all Languages and Departments are 
sent gratis on application. 

A very rich Collection of Bibliographical Material combined with wide-spread 
connections enable the subscriber to give prompt information in reply to 
most inquiries touching the literary productions of all countries of the globe. 



^telBT©^* SS «fc S4r FraixlsLfort St.. ISg-^^ "SToxrlsi 



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